Welcome to Abella 2.0.5-dev.
Abella < Kind name, action, proc type.

Abella < Import "ccs_core".
Importing from "ccs_core".
Warning: Definition can be used to defeat stratification
 (higher-order argument "Tech" occurs to the left of ->)
Warning: Definition can be used to defeat stratification
 (higher-order argument "Rel" occurs to the left of ->)
Warning: Definition can be used to defeat stratification
 (higher-order argument "Rel" occurs to the left of ->)

Abella < Define inv : proc -> proc -> prop by 
inv P Q := bisim_up_to refl_t P Q;
inv (par P1 Q1) (par P2 Q2) := inv P1 P2 /\ inv Q1 Q2.

Abella < Define bisim_inv : proc -> proc -> prop by 
bisim_inv P Q := (forall A P1, one P A P1 -> (exists Q1, one Q A Q1 /\ inv P1 Q1)) /\
  (forall A Q1, one Q A Q1 -> (exists P1, one P A P1 /\ inv P1 Q1)).

Abella < Theorem inv_bisim_inv : 
forall P Q, inv P Q -> bisim_inv P Q.


============================
 forall P Q, inv P Q -> bisim_inv P Q

inv_bisim_inv < induction on 1.

IH : forall P Q, inv P Q * -> bisim_inv P Q
============================
 forall P Q, inv P Q @ -> bisim_inv P Q

inv_bisim_inv < intros.

Variables: P Q
IH : forall P Q, inv P Q * -> bisim_inv P Q
H1 : inv P Q @
============================
 bisim_inv P Q

inv_bisim_inv < case H1.
Subgoal 1:

Variables: P Q
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : bisim_up_to refl_t P Q
============================
 bisim_inv P Q

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < case H2.
Subgoal 1:

Variables: P Q
IH : forall P Q, inv P Q * -> bisim_inv P Q
H3 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
============================
 bisim_inv P Q

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < unfold.
Subgoal 1.1:

Variables: P Q
IH : forall P Q, inv P Q * -> bisim_inv P Q
H3 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
============================
 forall A P1, one P A P1 -> (exists Q1, one Q A Q1 /\ inv P1 Q1)

Subgoal 1.2 is:
 forall A Q1, one Q A Q1 -> (exists P1, one P A P1 /\ inv P1 Q1)

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < intros.
Subgoal 1.1:

Variables: P Q A P1
IH : forall P Q, inv P Q * -> bisim_inv P Q
H3 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P1
============================
 exists Q1, one Q A Q1 /\ inv P1 Q1

Subgoal 1.2 is:
 forall A Q1, one Q A Q1 -> (exists P1, one P A P1 /\ inv P1 Q1)

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < apply H3 to H5.
Subgoal 1.1:

Variables: P Q A P1 Q2 P3 Q3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H3 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P1
H6 : one Q A Q2
H7 : refl_t P1 P3 Q2 Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists Q1, one Q A Q1 /\ inv P1 Q1

Subgoal 1.2 is:
 forall A Q1, one Q A Q1 -> (exists P1, one P A P1 /\ inv P1 Q1)

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < case H7.
Subgoal 1.1:

Variables: P Q A P3 Q3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H3 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists Q1, one Q A Q1 /\ inv P3 Q1

Subgoal 1.2 is:
 forall A Q1, one Q A Q1 -> (exists P1, one P A P1 /\ inv P1 Q1)

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < witness Q3.
Subgoal 1.1:

Variables: P Q A P3 Q3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H3 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 one Q A Q3 /\ inv P3 Q3

Subgoal 1.2 is:
 forall A Q1, one Q A Q1 -> (exists P1, one P A P1 /\ inv P1 Q1)

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < search.
Subgoal 1.2:

Variables: P Q
IH : forall P Q, inv P Q * -> bisim_inv P Q
H3 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
============================
 forall A Q1, one Q A Q1 -> (exists P1, one P A P1 /\ inv P1 Q1)

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < intros.
Subgoal 1.2:

Variables: P Q A Q1
IH : forall P Q, inv P Q * -> bisim_inv P Q
H3 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q1
============================
 exists P1, one P A P1 /\ inv P1 Q1

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < apply H4 to H5.
Subgoal 1.2:

Variables: P Q A Q1 P2 P3 Q3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H3 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q1
H6 : one P A P2
H7 : refl_t P2 P3 Q1 Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists P1, one P A P1 /\ inv P1 Q1

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < case H7.
Subgoal 1.2:

Variables: P Q A P3 Q3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H3 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists P1, one P A P1 /\ inv P1 Q3

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < witness P3.
Subgoal 1.2:

Variables: P Q A P3 Q3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H3 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 one P A P3 /\ inv P3 Q3

Subgoal 2 is:
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < search.
Subgoal 2:

Variables: Q2 P2 Q1 P1
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
============================
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < apply IH to H2.
Subgoal 2:

Variables: Q2 P2 Q1 P1
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H4 : bisim_inv P1 P2
============================
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < apply IH to H3.
Subgoal 2:

Variables: Q2 P2 Q1 P1
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H4 : bisim_inv P1 P2
H5 : bisim_inv Q1 Q2
============================
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < case H4.
Subgoal 2:

Variables: Q2 P2 Q1 P1
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H5 : bisim_inv Q1 Q2
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
============================
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < case H5.
Subgoal 2:

Variables: Q2 P2 Q1 P1
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
============================
 bisim_inv (par P1 Q1) (par P2 Q2)

inv_bisim_inv < unfold.
Subgoal 2.1:

Variables: Q2 P2 Q1 P1
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
============================
 forall A P3, one (par P1 Q1) A P3 ->
   (exists Q3, one (par P2 Q2) A Q3 /\ inv P3 Q3)

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < intros.
Subgoal 2.1:

Variables: Q2 P2 Q1 P1 A P3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H10 : one (par P1 Q1) A P3
============================
 exists Q3, one (par P2 Q2) A Q3 /\ inv P3 Q3

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < case H10.
Subgoal 2.1.1:

Variables: Q2 P2 Q1 P1 A P5
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P1 A P5
============================
 exists Q3, one (par P2 Q2) A Q3 /\ inv (par P5 Q1) Q3

Subgoal 2.1.2 is:
 exists Q3, one (par P2 Q2) A Q3 /\ inv (par P1 Q4) Q3

Subgoal 2.1.3 is:
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.1.4 is:
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < apply H6 to H11.
Subgoal 2.1.1:

Variables: Q2 P2 Q1 P1 A P5 Q3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P1 A P5
H12 : one P2 A Q3
H13 : inv P5 Q3
============================
 exists Q3, one (par P2 Q2) A Q3 /\ inv (par P5 Q1) Q3

Subgoal 2.1.2 is:
 exists Q3, one (par P2 Q2) A Q3 /\ inv (par P1 Q4) Q3

Subgoal 2.1.3 is:
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.1.4 is:
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < search.
Subgoal 2.1.2:

Variables: Q2 P2 Q1 P1 A Q4
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one Q1 A Q4
============================
 exists Q3, one (par P2 Q2) A Q3 /\ inv (par P1 Q4) Q3

Subgoal 2.1.3 is:
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.1.4 is:
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < apply H8 to H11.
Subgoal 2.1.2:

Variables: Q2 P2 Q1 P1 A Q4 Q3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one Q1 A Q4
H12 : one Q2 A Q3
H13 : inv Q4 Q3
============================
 exists Q3, one (par P2 Q2) A Q3 /\ inv (par P1 Q4) Q3

Subgoal 2.1.3 is:
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.1.4 is:
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < search.
Subgoal 2.1.3:

Variables: Q2 P2 Q1 P1 X Q4 P5
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P1 (up X) P5
H12 : one Q1 (dn X) Q4
============================
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.1.4 is:
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < apply H6 to H11.
Subgoal 2.1.3:

Variables: Q2 P2 Q1 P1 X Q4 P5 Q3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P1 (up X) P5
H12 : one Q1 (dn X) Q4
H13 : one P2 (up X) Q3
H14 : inv P5 Q3
============================
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.1.4 is:
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < apply H8 to H12.
Subgoal 2.1.3:

Variables: Q2 P2 Q1 P1 X Q4 P5 Q3 Q5
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P1 (up X) P5
H12 : one Q1 (dn X) Q4
H13 : one P2 (up X) Q3
H14 : inv P5 Q3
H15 : one Q2 (dn X) Q5
H16 : inv Q4 Q5
============================
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.1.4 is:
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < search.
Subgoal 2.1.4:

Variables: Q2 P2 Q1 P1 X Q4 P5
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P1 (dn X) P5
H12 : one Q1 (up X) Q4
============================
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < apply H6 to H11.
Subgoal 2.1.4:

Variables: Q2 P2 Q1 P1 X Q4 P5 Q3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P1 (dn X) P5
H12 : one Q1 (up X) Q4
H13 : one P2 (dn X) Q3
H14 : inv P5 Q3
============================
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < apply H8 to H12.
Subgoal 2.1.4:

Variables: Q2 P2 Q1 P1 X Q4 P5 Q3 Q5
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P1 (dn X) P5
H12 : one Q1 (up X) Q4
H13 : one P2 (dn X) Q3
H14 : inv P5 Q3
H15 : one Q2 (up X) Q5
H16 : inv Q4 Q5
============================
 exists Q3, one (par P2 Q2) tau Q3 /\ inv (par P5 Q4) Q3

Subgoal 2.2 is:
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < search.
Subgoal 2.2:

Variables: Q2 P2 Q1 P1
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
============================
 forall A Q3, one (par P2 Q2) A Q3 ->
   (exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3)

inv_bisim_inv < intros.
Subgoal 2.2:

Variables: Q2 P2 Q1 P1 A Q3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H10 : one (par P2 Q2) A Q3
============================
 exists P3, one (par P1 Q1) A P3 /\ inv P3 Q3

inv_bisim_inv < case H10.
Subgoal 2.2.1:

Variables: Q2 P2 Q1 P1 A P4
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P2 A P4
============================
 exists P3, one (par P1 Q1) A P3 /\ inv P3 (par P4 Q2)

Subgoal 2.2.2 is:
 exists P3, one (par P1 Q1) A P3 /\ inv P3 (par P2 Q5)

Subgoal 2.2.3 is:
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

Subgoal 2.2.4 is:
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

inv_bisim_inv < apply H7 to H11.
Subgoal 2.2.1:

Variables: Q2 P2 Q1 P1 A P4 P3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P2 A P4
H12 : one P1 A P3
H13 : inv P3 P4
============================
 exists P3, one (par P1 Q1) A P3 /\ inv P3 (par P4 Q2)

Subgoal 2.2.2 is:
 exists P3, one (par P1 Q1) A P3 /\ inv P3 (par P2 Q5)

Subgoal 2.2.3 is:
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

Subgoal 2.2.4 is:
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

inv_bisim_inv < search.
Subgoal 2.2.2:

Variables: Q2 P2 Q1 P1 A Q5
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one Q2 A Q5
============================
 exists P3, one (par P1 Q1) A P3 /\ inv P3 (par P2 Q5)

Subgoal 2.2.3 is:
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

Subgoal 2.2.4 is:
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

inv_bisim_inv < apply H9 to H11.
Subgoal 2.2.2:

Variables: Q2 P2 Q1 P1 A Q5 P3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one Q2 A Q5
H12 : one Q1 A P3
H13 : inv P3 Q5
============================
 exists P3, one (par P1 Q1) A P3 /\ inv P3 (par P2 Q5)

Subgoal 2.2.3 is:
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

Subgoal 2.2.4 is:
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

inv_bisim_inv < search.
Subgoal 2.2.3:

Variables: Q2 P2 Q1 P1 X Q5 P4
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P2 (up X) P4
H12 : one Q2 (dn X) Q5
============================
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

Subgoal 2.2.4 is:
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

inv_bisim_inv < apply H7 to H11.
Subgoal 2.2.3:

Variables: Q2 P2 Q1 P1 X Q5 P4 P3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P2 (up X) P4
H12 : one Q2 (dn X) Q5
H13 : one P1 (up X) P3
H14 : inv P3 P4
============================
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

Subgoal 2.2.4 is:
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

inv_bisim_inv < apply H9 to H12.
Subgoal 2.2.3:

Variables: Q2 P2 Q1 P1 X Q5 P4 P3 P5
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P2 (up X) P4
H12 : one Q2 (dn X) Q5
H13 : one P1 (up X) P3
H14 : inv P3 P4
H15 : one Q1 (dn X) P5
H16 : inv P5 Q5
============================
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

Subgoal 2.2.4 is:
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

inv_bisim_inv < search.
Subgoal 2.2.4:

Variables: Q2 P2 Q1 P1 X Q5 P4
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P2 (dn X) P4
H12 : one Q2 (up X) Q5
============================
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

inv_bisim_inv < apply H7 to H11.
Subgoal 2.2.4:

Variables: Q2 P2 Q1 P1 X Q5 P4 P3
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P2 (dn X) P4
H12 : one Q2 (up X) Q5
H13 : one P1 (dn X) P3
H14 : inv P3 P4
============================
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

inv_bisim_inv < apply H9 to H12.
Subgoal 2.2.4:

Variables: Q2 P2 Q1 P1 X Q5 P4 P3 P5
IH : forall P Q, inv P Q * -> bisim_inv P Q
H2 : inv P1 P2 *
H3 : inv Q1 Q2 *
H6 : forall A P3, one P1 A P3 -> (exists Q1, one P2 A Q1 /\ inv P3 Q1)
H7 : forall A Q1, one P2 A Q1 -> (exists P3, one P1 A P3 /\ inv P3 Q1)
H8 : forall A P1, one Q1 A P1 -> (exists Q3, one Q2 A Q3 /\ inv P1 Q3)
H9 : forall A Q3, one Q2 A Q3 -> (exists P1, one Q1 A P1 /\ inv P1 Q3)
H11 : one P2 (dn X) P4
H12 : one Q2 (up X) Q5
H13 : one P1 (dn X) P3
H14 : inv P3 P4
H15 : one Q1 (up X) P5
H16 : inv P5 Q5
============================
 exists P3, one (par P1 Q1) tau P3 /\ inv P3 (par P4 Q5)

inv_bisim_inv < search.
Proof completed.
Abella < Theorem bisim_inv_bisim : 
forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q.


============================
 forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q

bisim_inv_bisim < coinduction.

CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
============================
 forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q #

bisim_inv_bisim < intros.

Variables: P Q
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H1 : bisim_inv P Q
============================
 bisim_up_to refl_t P Q #

bisim_inv_bisim < case H1.

Variables: P Q
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
============================
 bisim_up_to refl_t P Q #

bisim_inv_bisim < unfold.
Subgoal 1:

Variables: P Q
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
============================
 forall A P1, one P A P1 ->
   (exists Q1, one Q A Q1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

Subgoal 2 is:
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < intros.
Subgoal 1:

Variables: P Q A P1
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one P A P1
============================
 exists Q1, one Q A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +)

Subgoal 2 is:
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < apply H2 to H4.
Subgoal 1:

Variables: P Q A P1 Q2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one P A P1
H5 : one Q A Q2
H6 : inv P1 Q2
============================
 exists Q1, one Q A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +)

Subgoal 2 is:
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < witness Q2.
Subgoal 1:

Variables: P Q A P1 Q2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one P A P1
H5 : one Q A Q2
H6 : inv P1 Q2
============================
 one Q A Q2 /\
   (exists P2 Q1, refl_t P1 P2 Q2 Q1 /\ bisim_up_to refl_t P2 Q1 +)

Subgoal 2 is:
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < split.
Subgoal 1.1:

Variables: P Q A P1 Q2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one P A P1
H5 : one Q A Q2
H6 : inv P1 Q2
============================
 one Q A Q2

Subgoal 1.2 is:
 exists P2 Q1, refl_t P1 P2 Q2 Q1 /\ bisim_up_to refl_t P2 Q1 +

Subgoal 2 is:
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < search.
Subgoal 1.2:

Variables: P Q A P1 Q2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one P A P1
H5 : one Q A Q2
H6 : inv P1 Q2
============================
 exists P2 Q1, refl_t P1 P2 Q2 Q1 /\ bisim_up_to refl_t P2 Q1 +

Subgoal 2 is:
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < witness P1.
Subgoal 1.2:

Variables: P Q A P1 Q2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one P A P1
H5 : one Q A Q2
H6 : inv P1 Q2
============================
 exists Q1, refl_t P1 P1 Q2 Q1 /\ bisim_up_to refl_t P1 Q1 +

Subgoal 2 is:
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < witness Q2.
Subgoal 1.2:

Variables: P Q A P1 Q2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one P A P1
H5 : one Q A Q2
H6 : inv P1 Q2
============================
 refl_t P1 P1 Q2 Q2 /\ bisim_up_to refl_t P1 Q2 +

Subgoal 2 is:
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < split.
Subgoal 1.2.1:

Variables: P Q A P1 Q2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one P A P1
H5 : one Q A Q2
H6 : inv P1 Q2
============================
 refl_t P1 P1 Q2 Q2

Subgoal 1.2.2 is:
 bisim_up_to refl_t P1 Q2 +

Subgoal 2 is:
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < search.
Subgoal 1.2.2:

Variables: P Q A P1 Q2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one P A P1
H5 : one Q A Q2
H6 : inv P1 Q2
============================
 bisim_up_to refl_t P1 Q2 +

Subgoal 2 is:
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < apply inv_bisim_inv to H6.
Subgoal 1.2.2:

Variables: P Q A P1 Q2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one P A P1
H5 : one Q A Q2
H6 : inv P1 Q2
H7 : bisim_inv P1 Q2
============================
 bisim_up_to refl_t P1 Q2 +

Subgoal 2 is:
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < backchain CH.
Subgoal 2:

Variables: P Q
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
============================
 forall A Q1, one Q A Q1 ->
   (exists P1, one P A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +))

bisim_inv_bisim < intros.
Subgoal 2:

Variables: P Q A Q1
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one Q A Q1
============================
 exists P1, one P A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +)

bisim_inv_bisim < apply H3 to H4.
Subgoal 2:

Variables: P Q A Q1 P2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one Q A Q1
H5 : one P A P2
H6 : inv P2 Q1
============================
 exists P1, one P A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +)

bisim_inv_bisim < witness P2.
Subgoal 2:

Variables: P Q A Q1 P2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one Q A Q1
H5 : one P A P2
H6 : inv P2 Q1
============================
 one P A P2 /\
   (exists P1 Q2, refl_t P2 P1 Q1 Q2 /\ bisim_up_to refl_t P1 Q2 +)

bisim_inv_bisim < split.
Subgoal 2.1:

Variables: P Q A Q1 P2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one Q A Q1
H5 : one P A P2
H6 : inv P2 Q1
============================
 one P A P2

Subgoal 2.2 is:
 exists P1 Q2, refl_t P2 P1 Q1 Q2 /\ bisim_up_to refl_t P1 Q2 +

bisim_inv_bisim < search.
Subgoal 2.2:

Variables: P Q A Q1 P2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one Q A Q1
H5 : one P A P2
H6 : inv P2 Q1
============================
 exists P1 Q2, refl_t P2 P1 Q1 Q2 /\ bisim_up_to refl_t P1 Q2 +

bisim_inv_bisim < witness P2.
Subgoal 2.2:

Variables: P Q A Q1 P2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one Q A Q1
H5 : one P A P2
H6 : inv P2 Q1
============================
 exists Q2, refl_t P2 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2 +

bisim_inv_bisim < witness Q1.
Subgoal 2.2:

Variables: P Q A Q1 P2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one Q A Q1
H5 : one P A P2
H6 : inv P2 Q1
============================
 refl_t P2 P2 Q1 Q1 /\ bisim_up_to refl_t P2 Q1 +

bisim_inv_bisim < split.
Subgoal 2.2.1:

Variables: P Q A Q1 P2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one Q A Q1
H5 : one P A P2
H6 : inv P2 Q1
============================
 refl_t P2 P2 Q1 Q1

Subgoal 2.2.2 is:
 bisim_up_to refl_t P2 Q1 +

bisim_inv_bisim < search.
Subgoal 2.2.2:

Variables: P Q A Q1 P2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one Q A Q1
H5 : one P A P2
H6 : inv P2 Q1
============================
 bisim_up_to refl_t P2 Q1 +

bisim_inv_bisim < apply inv_bisim_inv to H6.
Subgoal 2.2.2:

Variables: P Q A Q1 P2
CH : forall P Q, bisim_inv P Q -> bisim_up_to refl_t P Q +
H2 : forall A P2, one P A P2 -> (exists Q2, one Q A Q2 /\ inv P2 Q2)
H3 : forall A Q2, one Q A Q2 -> (exists P2, one P A P2 /\ inv P2 Q2)
H4 : one Q A Q1
H5 : one P A P2
H6 : inv P2 Q1
H7 : bisim_inv P2 Q1
============================
 bisim_up_to refl_t P2 Q1 +

bisim_inv_bisim < backchain CH.
Proof completed.
Abella < Theorem bisim_par_subst_1 : 
forall P Q R, bisim_up_to refl_t P Q ->
  bisim_up_to refl_t (par P R) (par Q R).


============================
 forall P Q R, bisim_up_to refl_t P Q ->
   bisim_up_to refl_t (par P R) (par Q R)

bisim_par_subst_1 < intros.

Variables: P Q R
H1 : bisim_up_to refl_t P Q
============================
 bisim_up_to refl_t (par P R) (par Q R)

bisim_par_subst_1 < apply bisim_reflexive_ with P = R.

Variables: P Q R
H1 : bisim_up_to refl_t P Q
H2 : bisim_up_to refl_t R R
============================
 bisim_up_to refl_t (par P R) (par Q R)

bisim_par_subst_1 < backchain bisim_inv_bisim.

Variables: P Q R
H1 : bisim_up_to refl_t P Q
H2 : bisim_up_to refl_t R R
============================
 bisim_inv (par P R) (par Q R)

bisim_par_subst_1 < backchain inv_bisim_inv.
Proof completed.
Abella < Theorem bisim_par_subst_2 : 
forall P Q R, bisim_up_to refl_t P Q ->
  bisim_up_to refl_t (par R P) (par R Q).


============================
 forall P Q R, bisim_up_to refl_t P Q ->
   bisim_up_to refl_t (par R P) (par R Q)

bisim_par_subst_2 < intros.

Variables: P Q R
H1 : bisim_up_to refl_t P Q
============================
 bisim_up_to refl_t (par R P) (par R Q)

bisim_par_subst_2 < apply bisim_reflexive_ with P = R.

Variables: P Q R
H1 : bisim_up_to refl_t P Q
H2 : bisim_up_to refl_t R R
============================
 bisim_up_to refl_t (par R P) (par R Q)

bisim_par_subst_2 < backchain bisim_inv_bisim.

Variables: P Q R
H1 : bisim_up_to refl_t P Q
H2 : bisim_up_to refl_t R R
============================
 bisim_inv (par R P) (par R Q)

bisim_par_subst_2 < backchain inv_bisim_inv.
Proof completed.
Abella < Theorem bisim_plus_subst_1 : 
forall P Q R, bisim_up_to refl_t P Q ->
  bisim_up_to refl_t (plus P R) (plus Q R).


============================
 forall P Q R, bisim_up_to refl_t P Q ->
   bisim_up_to refl_t (plus P R) (plus Q R)

bisim_plus_subst_1 < intros.

Variables: P Q R
H1 : bisim_up_to refl_t P Q
============================
 bisim_up_to refl_t (plus P R) (plus Q R)

bisim_plus_subst_1 < case H1.

Variables: P Q R
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
============================
 bisim_up_to refl_t (plus P R) (plus Q R)

bisim_plus_subst_1 < unfold.
Subgoal 1:

Variables: P Q R
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
============================
 forall A P1, one (plus P R) A P1 ->
   (exists Q1, one (plus Q R) A Q1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < intros.
Subgoal 1:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : one (plus P R) A P1
============================
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < case H4.
Subgoal 1.1:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P1
============================
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 1.2 is:
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < apply H2 to H5.
Subgoal 1.1:

Variables: P Q R A P1 Q2 P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P1
H6 : one Q A Q2
H7 : refl_t P1 P3 Q2 Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 1.2 is:
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < case H7.
Subgoal 1.1:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P3 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 1.2 is:
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < witness Q3.
Subgoal 1.1:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 one (plus Q R) A Q3 /\
   (exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 1.2 is:
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < split.
Subgoal 1.1.1:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 one (plus Q R) A Q3

Subgoal 1.1.2 is:
 exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 1.2 is:
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < search.
Subgoal 1.1.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 1.2 is:
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < witness P3.
Subgoal 1.1.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists Q2, refl_t P3 P3 Q3 Q2 /\ bisim_up_to refl_t P3 Q2

Subgoal 1.2 is:
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < witness Q3.
Subgoal 1.1.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 refl_t P3 P3 Q3 Q3 /\ bisim_up_to refl_t P3 Q3

Subgoal 1.2 is:
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < search.
Subgoal 1.2:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 exists Q1, one (plus Q R) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < witness P1.
Subgoal 1.2:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 one (plus Q R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 P1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < split.
Subgoal 1.2.1:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 one (plus Q R) A P1

Subgoal 1.2.2 is:
 exists P2 Q2, refl_t P1 P2 P1 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < search.
Subgoal 1.2.2:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 exists P2 Q2, refl_t P1 P2 P1 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < witness P1.
Subgoal 1.2.2:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 exists Q2, refl_t P1 P1 P1 Q2 /\ bisim_up_to refl_t P1 Q2

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < witness P1.
Subgoal 1.2.2:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 refl_t P1 P1 P1 P1 /\ bisim_up_to refl_t P1 P1

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < apply bisim_reflexive_ with P = P1.
Subgoal 1.2.2:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
H6 : bisim_up_to refl_t P1 P1
============================
 refl_t P1 P1 P1 P1 /\ bisim_up_to refl_t P1 P1

Subgoal 2 is:
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < search.
Subgoal 2:

Variables: P Q R
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
============================
 forall A Q1, one (plus Q R) A Q1 ->
   (exists P1, one (plus P R) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_1 < intros.
Subgoal 2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : one (plus Q R) A Q1
============================
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_1 < case H4.
Subgoal 2.1:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q1
============================
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2.2 is:
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_1 < apply H3 to H5.
Subgoal 2.1:

Variables: P Q R A Q1 P2 P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q1
H6 : one P A P2
H7 : refl_t P2 P3 Q1 Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2.2 is:
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_1 < case H7.
Subgoal 2.1:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2.2 is:
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_1 < witness P3.
Subgoal 2.1:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 one (plus P R) A P3 /\
   (exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2.2 is:
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_1 < split.
Subgoal 2.1.1:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 one (plus P R) A P3

Subgoal 2.1.2 is:
 exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 2.2 is:
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_1 < search.
Subgoal 2.1.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 2.2 is:
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_1 < witness P2.
Subgoal 2.1.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists Q2, refl_t P3 P3 Q3 Q2 /\ bisim_up_to refl_t P3 Q2

Subgoal 2.2 is:
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_1 < witness Q3.
Subgoal 2.1.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 refl_t P3 P3 Q3 Q3 /\ bisim_up_to refl_t P3 Q3

Subgoal 2.2 is:
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_1 < search.
Subgoal 2.2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 exists P1, one (plus P R) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_1 < witness Q1.
Subgoal 2.2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 one (plus P R) A Q1 /\
   (exists P2 Q2, refl_t Q1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_1 < split.
Subgoal 2.2.1:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 one (plus P R) A Q1

Subgoal 2.2.2 is:
 exists P2 Q2, refl_t Q1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2

bisim_plus_subst_1 < search.
Subgoal 2.2.2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 exists P2 Q2, refl_t Q1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2

bisim_plus_subst_1 < witness Q1.
Subgoal 2.2.2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 exists Q2, refl_t Q1 Q1 Q1 Q2 /\ bisim_up_to refl_t Q1 Q2

bisim_plus_subst_1 < witness Q1.
Subgoal 2.2.2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 refl_t Q1 Q1 Q1 Q1 /\ bisim_up_to refl_t Q1 Q1

bisim_plus_subst_1 < apply bisim_reflexive_ with P = Q1.
Subgoal 2.2.2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
H6 : bisim_up_to refl_t Q1 Q1
============================
 refl_t Q1 Q1 Q1 Q1 /\ bisim_up_to refl_t Q1 Q1

bisim_plus_subst_1 < search.
Proof completed.
Abella < Theorem bisim_plus_subst_2 : 
forall P Q R, bisim_up_to refl_t P Q ->
  bisim_up_to refl_t (plus R P) (plus R Q).


============================
 forall P Q R, bisim_up_to refl_t P Q ->
   bisim_up_to refl_t (plus R P) (plus R Q)

bisim_plus_subst_2 < intros.

Variables: P Q R
H1 : bisim_up_to refl_t P Q
============================
 bisim_up_to refl_t (plus R P) (plus R Q)

bisim_plus_subst_2 < case H1.

Variables: P Q R
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
============================
 bisim_up_to refl_t (plus R P) (plus R Q)

bisim_plus_subst_2 < unfold.
Subgoal 1:

Variables: P Q R
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
============================
 forall A P1, one (plus R P) A P1 ->
   (exists Q1, one (plus R Q) A Q1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < intros.
Subgoal 1:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : one (plus R P) A P1
============================
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < case H4.
Subgoal 1.1:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 1.2 is:
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < witness P1.
Subgoal 1.1:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 one (plus R Q) A P1 /\
   (exists P2 Q2, refl_t P1 P2 P1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 1.2 is:
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < split.
Subgoal 1.1.1:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 one (plus R Q) A P1

Subgoal 1.1.2 is:
 exists P2 Q2, refl_t P1 P2 P1 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 1.2 is:
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < search.
Subgoal 1.1.2:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 exists P2 Q2, refl_t P1 P2 P1 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 1.2 is:
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < witness P1.
Subgoal 1.1.2:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 exists Q2, refl_t P1 P1 P1 Q2 /\ bisim_up_to refl_t P1 Q2

Subgoal 1.2 is:
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < witness P1.
Subgoal 1.1.2:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
============================
 refl_t P1 P1 P1 P1 /\ bisim_up_to refl_t P1 P1

Subgoal 1.2 is:
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < apply bisim_reflexive_ with P = P1.
Subgoal 1.1.2:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A P1
H6 : bisim_up_to refl_t P1 P1
============================
 refl_t P1 P1 P1 P1 /\ bisim_up_to refl_t P1 P1

Subgoal 1.2 is:
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < search.
Subgoal 1.2:

Variables: P Q R A P1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P1
============================
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < apply H2 to H5.
Subgoal 1.2:

Variables: P Q R A P1 Q2 P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P1
H6 : one Q A Q2
H7 : refl_t P1 P3 Q2 Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < case H7.
Subgoal 1.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists Q1, one (plus R Q) A Q1 /\
   (exists P2 Q2, refl_t P3 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < witness Q3.
Subgoal 1.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 one (plus R Q) A Q3 /\
   (exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < split.
Subgoal 1.2.1:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 one (plus R Q) A Q3

Subgoal 1.2.2 is:
 exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < search.
Subgoal 1.2.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < witness P3.
Subgoal 1.2.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists Q2, refl_t P3 P3 Q3 Q2 /\ bisim_up_to refl_t P3 Q2

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < witness Q3.
Subgoal 1.2.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one P A P3
H6 : one Q A Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 refl_t P3 P3 Q3 Q3 /\ bisim_up_to refl_t P3 Q3

Subgoal 2 is:
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < search.
Subgoal 2:

Variables: P Q R
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
============================
 forall A Q1, one (plus R Q) A Q1 ->
   (exists P1, one (plus R P) A P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_plus_subst_2 < intros.
Subgoal 2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H4 : one (plus R Q) A Q1
============================
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < case H4.
Subgoal 2.1:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2.2 is:
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < witness Q1.
Subgoal 2.1:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 one (plus R P) A Q1 /\
   (exists P2 Q2, refl_t Q1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2.2 is:
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < split.
Subgoal 2.1.1:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 one (plus R P) A Q1

Subgoal 2.1.2 is:
 exists P2 Q2, refl_t Q1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 2.2 is:
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < search.
Subgoal 2.1.2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 exists P2 Q2, refl_t Q1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 2.2 is:
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < witness Q1.
Subgoal 2.1.2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 exists Q2, refl_t Q1 Q1 Q1 Q2 /\ bisim_up_to refl_t Q1 Q2

Subgoal 2.2 is:
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < witness Q1.
Subgoal 2.1.2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
============================
 refl_t Q1 Q1 Q1 Q1 /\ bisim_up_to refl_t Q1 Q1

Subgoal 2.2 is:
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < apply bisim_reflexive_ with P = Q1.
Subgoal 2.1.2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one R A Q1
H6 : bisim_up_to refl_t Q1 Q1
============================
 refl_t Q1 Q1 Q1 Q1 /\ bisim_up_to refl_t Q1 Q1

Subgoal 2.2 is:
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < search.
Subgoal 2.2:

Variables: P Q R A Q1
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q1
============================
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < apply H3 to H5.
Subgoal 2.2:

Variables: P Q R A Q1 P2 P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q1
H6 : one P A P2
H7 : refl_t P2 P3 Q1 Q3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < case H7.
Subgoal 2.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists P1, one (plus R P) A P1 /\
   (exists P2 Q2, refl_t P1 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < witness P3.
Subgoal 2.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 one (plus R P) A P3 /\
   (exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_plus_subst_2 < split.
Subgoal 2.2.1:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 one (plus R P) A P3

Subgoal 2.2.2 is:
 exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2

bisim_plus_subst_2 < search.
Subgoal 2.2.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists P2 Q2, refl_t P3 P2 Q3 Q2 /\ bisim_up_to refl_t P2 Q2

bisim_plus_subst_2 < witness P2.
Subgoal 2.2.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 exists Q2, refl_t P3 P3 Q3 Q2 /\ bisim_up_to refl_t P3 Q2

bisim_plus_subst_2 < witness Q3.
Subgoal 2.2.2:

Variables: P Q R A P3 Q3
H2 : forall A P2, one P A P2 ->
       (exists Q2, one Q A Q2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H3 : forall A Q2, one Q A Q2 ->
       (exists P2, one P A P2 /\
            (exists P3 Q3, refl_t P2 P3 Q2 Q3 /\ bisim_up_to refl_t P3 Q3))
H5 : one Q A Q3
H6 : one P A P3
H8 : bisim_up_to refl_t P3 Q3
============================
 refl_t P3 P3 Q3 Q3 /\ bisim_up_to refl_t P3 Q3

bisim_plus_subst_2 < search.
Proof completed.
Abella < Theorem bisim_act_subst : 
forall P Q A, bisim_up_to refl_t P Q ->
  bisim_up_to refl_t (act A P) (act A Q).


============================
 forall P Q A, bisim_up_to refl_t P Q ->
   bisim_up_to refl_t (act A P) (act A Q)

bisim_act_subst < intros.

Variables: P Q A
H1 : bisim_up_to refl_t P Q
============================
 bisim_up_to refl_t (act A P) (act A Q)

bisim_act_subst < unfold.
Subgoal 1:

Variables: P Q A
H1 : bisim_up_to refl_t P Q
============================
 forall A1 P1, one (act A P) A1 P1 ->
   (exists Q1, one (act A Q) A1 Q1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

Subgoal 2 is:
 forall A1 Q1, one (act A Q) A1 Q1 ->
   (exists P1, one (act A P) A1 P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_act_subst < intros.
Subgoal 1:

Variables: P Q A A1 P1
H1 : bisim_up_to refl_t P Q
H2 : one (act A P) A1 P1
============================
 exists Q1, one (act A Q) A1 Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A1 Q1, one (act A Q) A1 Q1 ->
   (exists P1, one (act A P) A1 P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_act_subst < case H2.
Subgoal 1:

Variables: Q A1 P1
H1 : bisim_up_to refl_t P1 Q
============================
 exists Q1, one (act A1 Q) A1 Q1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A1 Q1, one (act A Q) A1 Q1 ->
   (exists P1, one (act A P) A1 P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_act_subst < witness Q.
Subgoal 1:

Variables: Q A1 P1
H1 : bisim_up_to refl_t P1 Q
============================
 one (act A1 Q) A1 Q /\
   (exists P2 Q2, refl_t P1 P2 Q Q2 /\ bisim_up_to refl_t P2 Q2)

Subgoal 2 is:
 forall A1 Q1, one (act A Q) A1 Q1 ->
   (exists P1, one (act A P) A1 P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_act_subst < split.
Subgoal 1.1:

Variables: Q A1 P1
H1 : bisim_up_to refl_t P1 Q
============================
 one (act A1 Q) A1 Q

Subgoal 1.2 is:
 exists P2 Q2, refl_t P1 P2 Q Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 2 is:
 forall A1 Q1, one (act A Q) A1 Q1 ->
   (exists P1, one (act A P) A1 P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_act_subst < search.
Subgoal 1.2:

Variables: Q A1 P1
H1 : bisim_up_to refl_t P1 Q
============================
 exists P2 Q2, refl_t P1 P2 Q Q2 /\ bisim_up_to refl_t P2 Q2

Subgoal 2 is:
 forall A1 Q1, one (act A Q) A1 Q1 ->
   (exists P1, one (act A P) A1 P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_act_subst < witness P1.
Subgoal 1.2:

Variables: Q A1 P1
H1 : bisim_up_to refl_t P1 Q
============================
 exists Q2, refl_t P1 P1 Q Q2 /\ bisim_up_to refl_t P1 Q2

Subgoal 2 is:
 forall A1 Q1, one (act A Q) A1 Q1 ->
   (exists P1, one (act A P) A1 P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_act_subst < witness Q.
Subgoal 1.2:

Variables: Q A1 P1
H1 : bisim_up_to refl_t P1 Q
============================
 refl_t P1 P1 Q Q /\ bisim_up_to refl_t P1 Q

Subgoal 2 is:
 forall A1 Q1, one (act A Q) A1 Q1 ->
   (exists P1, one (act A P) A1 P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_act_subst < search.
Subgoal 2:

Variables: P Q A
H1 : bisim_up_to refl_t P Q
============================
 forall A1 Q1, one (act A Q) A1 Q1 ->
   (exists P1, one (act A P) A1 P1 /\
        (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2))

bisim_act_subst < intros.
Subgoal 2:

Variables: P Q A A1 Q1
H1 : bisim_up_to refl_t P Q
H2 : one (act A Q) A1 Q1
============================
 exists P1, one (act A P) A1 P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_act_subst < case H2.
Subgoal 2:

Variables: P A1 Q1
H1 : bisim_up_to refl_t P Q1
============================
 exists P1, one (act A1 P) A1 P1 /\
   (exists P2 Q2, refl_t P1 P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_act_subst < witness P.
Subgoal 2:

Variables: P A1 Q1
H1 : bisim_up_to refl_t P Q1
============================
 one (act A1 P) A1 P /\
   (exists P2 Q2, refl_t P P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2)

bisim_act_subst < split.
Subgoal 2.1:

Variables: P A1 Q1
H1 : bisim_up_to refl_t P Q1
============================
 one (act A1 P) A1 P

Subgoal 2.2 is:
 exists P2 Q2, refl_t P P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2

bisim_act_subst < search.
Subgoal 2.2:

Variables: P A1 Q1
H1 : bisim_up_to refl_t P Q1
============================
 exists P2 Q2, refl_t P P2 Q1 Q2 /\ bisim_up_to refl_t P2 Q2

bisim_act_subst < witness P.
Subgoal 2.2:

Variables: P A1 Q1
H1 : bisim_up_to refl_t P Q1
============================
 exists Q2, refl_t P P Q1 Q2 /\ bisim_up_to refl_t P Q2

bisim_act_subst < witness Q1.
Subgoal 2.2:

Variables: P A1 Q1
H1 : bisim_up_to refl_t P Q1
============================
 refl_t P P Q1 Q1 /\ bisim_up_to refl_t P Q1

bisim_act_subst < search.
Proof completed.
Abella < Kind ctx type.

Abella < Type hole ctx.

Abella < Type plus_l, par_l ctx -> proc -> ctx.

Abella < Type plus_r, par_r proc -> ctx -> ctx.

Abella < Type act_d action -> ctx -> ctx.

Abella < Define at : ctx -> proc -> proc -> prop by 
at hole P P;
at (plus_l C R) P (plus Q R) := at C P Q;
at (plus_r R C) P (plus R Q) := at C P Q;
at (par_l C R) P (par Q R) := at C P Q;
at (par_r R C) P (par R Q) := at C P Q;
at (act_d A C) P (act A Q) := at C P Q.

Abella < Define substitutive_rel : (proc -> proc -> prop) -> prop by 
substitutive_rel Rel := forall P1 P2 C Q1 Q2, at C P1 Q1 -> at C P2 Q2 -> Rel P1 P2 -> Rel Q1 Q2.
Warning: Definition can be used to defeat stratification
 (higher-order argument "Rel" occurs to the left of ->)

Abella < Theorem bisim_substitutive : 
substitutive_rel (bisim_up_to refl_t).


============================
 substitutive_rel (bisim_up_to refl_t)

bisim_substitutive < unfold.

============================
 forall P1 P2 C Q1 Q2, at C P1 Q1 -> at C P2 Q2 ->
   bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2

bisim_substitutive < induction on 1.

IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
============================
 forall P1 P2 C Q1 Q2, at C P1 Q1 @ -> at C P2 Q2 ->
   bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2

bisim_substitutive < intros.

Variables: P1 P2 C Q1 Q2
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H1 : at C P1 Q1 @
H2 : at C P2 Q2
H3 : bisim_up_to refl_t P1 P2
============================
 bisim_up_to refl_t Q1 Q2

bisim_substitutive < case H1.
Subgoal 1:

Variables: P2 Q1 Q2
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H2 : at hole P2 Q2
H3 : bisim_up_to refl_t Q1 P2
============================
 bisim_up_to refl_t Q1 Q2

Subgoal 2 is:
 bisim_up_to refl_t (plus Q R) Q2

Subgoal 3 is:
 bisim_up_to refl_t (plus R Q) Q2

Subgoal 4 is:
 bisim_up_to refl_t (par Q R) Q2

Subgoal 5 is:
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < case H2.
Subgoal 1:

Variables: Q1 Q2
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H3 : bisim_up_to refl_t Q1 Q2
============================
 bisim_up_to refl_t Q1 Q2

Subgoal 2 is:
 bisim_up_to refl_t (plus Q R) Q2

Subgoal 3 is:
 bisim_up_to refl_t (plus R Q) Q2

Subgoal 4 is:
 bisim_up_to refl_t (par Q R) Q2

Subgoal 5 is:
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < search.
Subgoal 2:

Variables: P1 P2 Q2 R Q C1
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H2 : at (plus_l C1 R) P2 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
============================
 bisim_up_to refl_t (plus Q R) Q2

Subgoal 3 is:
 bisim_up_to refl_t (plus R Q) Q2

Subgoal 4 is:
 bisim_up_to refl_t (par Q R) Q2

Subgoal 5 is:
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < case H2.
Subgoal 2:

Variables: P1 P2 R Q C1 Q3
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
H5 : at C1 P2 Q3
============================
 bisim_up_to refl_t (plus Q R) (plus Q3 R)

Subgoal 3 is:
 bisim_up_to refl_t (plus R Q) Q2

Subgoal 4 is:
 bisim_up_to refl_t (par Q R) Q2

Subgoal 5 is:
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < apply IH to H4 H5 H3.
Subgoal 2:

Variables: P1 P2 R Q C1 Q3
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
H5 : at C1 P2 Q3
H6 : bisim_up_to refl_t Q Q3
============================
 bisim_up_to refl_t (plus Q R) (plus Q3 R)

Subgoal 3 is:
 bisim_up_to refl_t (plus R Q) Q2

Subgoal 4 is:
 bisim_up_to refl_t (par Q R) Q2

Subgoal 5 is:
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < backchain bisim_plus_subst_1.
Subgoal 3:

Variables: P1 P2 Q2 Q R C1
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H2 : at (plus_r R C1) P2 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
============================
 bisim_up_to refl_t (plus R Q) Q2

Subgoal 4 is:
 bisim_up_to refl_t (par Q R) Q2

Subgoal 5 is:
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < case H2.
Subgoal 3:

Variables: P1 P2 Q R C1 Q3
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
H5 : at C1 P2 Q3
============================
 bisim_up_to refl_t (plus R Q) (plus R Q3)

Subgoal 4 is:
 bisim_up_to refl_t (par Q R) Q2

Subgoal 5 is:
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < apply IH to H4 H5 H3.
Subgoal 3:

Variables: P1 P2 Q R C1 Q3
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
H5 : at C1 P2 Q3
H6 : bisim_up_to refl_t Q Q3
============================
 bisim_up_to refl_t (plus R Q) (plus R Q3)

Subgoal 4 is:
 bisim_up_to refl_t (par Q R) Q2

Subgoal 5 is:
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < backchain bisim_plus_subst_2.
Subgoal 4:

Variables: P1 P2 Q2 R Q C1
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H2 : at (par_l C1 R) P2 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
============================
 bisim_up_to refl_t (par Q R) Q2

Subgoal 5 is:
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < case H2.
Subgoal 4:

Variables: P1 P2 R Q C1 Q3
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
H5 : at C1 P2 Q3
============================
 bisim_up_to refl_t (par Q R) (par Q3 R)

Subgoal 5 is:
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < apply IH to H4 H5 H3.
Subgoal 4:

Variables: P1 P2 R Q C1 Q3
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
H5 : at C1 P2 Q3
H6 : bisim_up_to refl_t Q Q3
============================
 bisim_up_to refl_t (par Q R) (par Q3 R)

Subgoal 5 is:
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < backchain bisim_par_subst_1.
Subgoal 5:

Variables: P1 P2 Q2 Q R C1
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H2 : at (par_r R C1) P2 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
============================
 bisim_up_to refl_t (par R Q) Q2

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < case H2.
Subgoal 5:

Variables: P1 P2 Q R C1 Q3
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
H5 : at C1 P2 Q3
============================
 bisim_up_to refl_t (par R Q) (par R Q3)

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < apply IH to H4 H5 H3.
Subgoal 5:

Variables: P1 P2 Q R C1 Q3
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
H5 : at C1 P2 Q3
H6 : bisim_up_to refl_t Q Q3
============================
 bisim_up_to refl_t (par R Q) (par R Q3)

Subgoal 6 is:
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < backchain bisim_par_subst_2.
Subgoal 6:

Variables: P1 P2 Q2 Q A C1
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H2 : at (act_d A C1) P2 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
============================
 bisim_up_to refl_t (act A Q) Q2

bisim_substitutive < case H2.
Subgoal 6:

Variables: P1 P2 Q A C1 Q3
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
H5 : at C1 P2 Q3
============================
 bisim_up_to refl_t (act A Q) (act A Q3)

bisim_substitutive < apply IH to H4 H5 H3.
Subgoal 6:

Variables: P1 P2 Q A C1 Q3
IH : forall P1 P2 C Q1 Q2, at C P1 Q1 * -> at C P2 Q2 ->
       bisim_up_to refl_t P1 P2 -> bisim_up_to refl_t Q1 Q2
H3 : bisim_up_to refl_t P1 P2
H4 : at C1 P1 Q *
H5 : at C1 P2 Q3
H6 : bisim_up_to refl_t Q Q3
============================
 bisim_up_to refl_t (act A Q) (act A Q3)

bisim_substitutive < backchain bisim_act_subst.
Proof completed.
Abella < Theorem at_det3 : 
forall C P Q1 Q2, at C P Q1 -> at C P Q2 -> Q1 = Q2.


============================
 forall C P Q1 Q2, at C P Q1 -> at C P Q2 -> Q1 = Q2

at_det3 < induction on 1.

IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
============================
 forall C P Q1 Q2, at C P Q1 @ -> at C P Q2 -> Q1 = Q2

at_det3 < intros.

Variables: C P Q1 Q2
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H1 : at C P Q1 @
H2 : at C P Q2
============================
 Q1 = Q2

at_det3 < case H1.
Subgoal 1:

Variables: Q1 Q2
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H2 : at hole Q1 Q2
============================
 Q1 = Q2

Subgoal 2 is:
 plus Q R = Q2

Subgoal 3 is:
 plus R Q = Q2

Subgoal 4 is:
 par Q R = Q2

Subgoal 5 is:
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < case H2.
Subgoal 1:

Variables: Q2
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
============================
 Q2 = Q2

Subgoal 2 is:
 plus Q R = Q2

Subgoal 3 is:
 plus R Q = Q2

Subgoal 4 is:
 par Q R = Q2

Subgoal 5 is:
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < search.
Subgoal 2:

Variables: P Q2 R Q C1
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H2 : at (plus_l C1 R) P Q2
H3 : at C1 P Q *
============================
 plus Q R = Q2

Subgoal 3 is:
 plus R Q = Q2

Subgoal 4 is:
 par Q R = Q2

Subgoal 5 is:
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < case H2.
Subgoal 2:

Variables: P R Q C1 Q3
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H3 : at C1 P Q *
H4 : at C1 P Q3
============================
 plus Q R = plus Q3 R

Subgoal 3 is:
 plus R Q = Q2

Subgoal 4 is:
 par Q R = Q2

Subgoal 5 is:
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < apply IH to H3 H4.
Subgoal 2:

Variables: P R C1 Q3
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H3 : at C1 P Q3 *
H4 : at C1 P Q3
============================
 plus Q3 R = plus Q3 R

Subgoal 3 is:
 plus R Q = Q2

Subgoal 4 is:
 par Q R = Q2

Subgoal 5 is:
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < search.
Subgoal 3:

Variables: P Q2 Q R C1
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H2 : at (plus_r R C1) P Q2
H3 : at C1 P Q *
============================
 plus R Q = Q2

Subgoal 4 is:
 par Q R = Q2

Subgoal 5 is:
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < case H2.
Subgoal 3:

Variables: P Q R C1 Q3
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H3 : at C1 P Q *
H4 : at C1 P Q3
============================
 plus R Q = plus R Q3

Subgoal 4 is:
 par Q R = Q2

Subgoal 5 is:
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < apply IH to H3 H4.
Subgoal 3:

Variables: P R C1 Q3
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H3 : at C1 P Q3 *
H4 : at C1 P Q3
============================
 plus R Q3 = plus R Q3

Subgoal 4 is:
 par Q R = Q2

Subgoal 5 is:
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < search.
Subgoal 4:

Variables: P Q2 R Q C1
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H2 : at (par_l C1 R) P Q2
H3 : at C1 P Q *
============================
 par Q R = Q2

Subgoal 5 is:
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < case H2.
Subgoal 4:

Variables: P R Q C1 Q3
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H3 : at C1 P Q *
H4 : at C1 P Q3
============================
 par Q R = par Q3 R

Subgoal 5 is:
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < apply IH to H3 H4.
Subgoal 4:

Variables: P R C1 Q3
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H3 : at C1 P Q3 *
H4 : at C1 P Q3
============================
 par Q3 R = par Q3 R

Subgoal 5 is:
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < search.
Subgoal 5:

Variables: P Q2 Q R C1
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H2 : at (par_r R C1) P Q2
H3 : at C1 P Q *
============================
 par R Q = Q2

Subgoal 6 is:
 act A Q = Q2

at_det3 < case H2.
Subgoal 5:

Variables: P Q R C1 Q3
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H3 : at C1 P Q *
H4 : at C1 P Q3
============================
 par R Q = par R Q3

Subgoal 6 is:
 act A Q = Q2

at_det3 < apply IH to H3 H4.
Subgoal 5:

Variables: P R C1 Q3
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H3 : at C1 P Q3 *
H4 : at C1 P Q3
============================
 par R Q3 = par R Q3

Subgoal 6 is:
 act A Q = Q2

at_det3 < search.
Subgoal 6:

Variables: P Q2 Q A C1
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H2 : at (act_d A C1) P Q2
H3 : at C1 P Q *
============================
 act A Q = Q2

at_det3 < case H2.
Subgoal 6:

Variables: P Q A C1 Q3
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H3 : at C1 P Q *
H4 : at C1 P Q3
============================
 act A Q = act A Q3

at_det3 < apply IH to H3 H4.
Subgoal 6:

Variables: P A C1 Q3
IH : forall C P Q1 Q2, at C P Q1 * -> at C P Q2 -> Q1 = Q2
H3 : at C1 P Q3 *
H4 : at C1 P Q3
============================
 act A Q3 = act A Q3

at_det3 < search.
Proof completed.
Abella < Theorem at_det2 : 
forall C P1 P2 Q, at C P1 Q -> at C P2 Q -> P1 = P2.


============================
 forall C P1 P2 Q, at C P1 Q -> at C P2 Q -> P1 = P2

at_det2 < induction on 1.

IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
============================
 forall C P1 P2 Q, at C P1 Q @ -> at C P2 Q -> P1 = P2

at_det2 < intros.

Variables: C P1 P2 Q
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H1 : at C P1 Q @
H2 : at C P2 Q
============================
 P1 = P2

at_det2 < case H1.
Subgoal 1:

Variables: P2 Q
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H2 : at hole P2 Q
============================
 Q = P2

Subgoal 2 is:
 P1 = P2

Subgoal 3 is:
 P1 = P2

Subgoal 4 is:
 P1 = P2

Subgoal 5 is:
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < case H2.
Subgoal 1:

Variables: Q
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
============================
 Q = Q

Subgoal 2 is:
 P1 = P2

Subgoal 3 is:
 P1 = P2

Subgoal 4 is:
 P1 = P2

Subgoal 5 is:
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < search.
Subgoal 2:

Variables: P1 P2 R Q1 C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H2 : at (plus_l C1 R) P2 (plus Q1 R)
H3 : at C1 P1 Q1 *
============================
 P1 = P2

Subgoal 3 is:
 P1 = P2

Subgoal 4 is:
 P1 = P2

Subgoal 5 is:
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < case H2.
Subgoal 2:

Variables: P1 P2 R Q1 C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H3 : at C1 P1 Q1 *
H4 : at C1 P2 Q1
============================
 P1 = P2

Subgoal 3 is:
 P1 = P2

Subgoal 4 is:
 P1 = P2

Subgoal 5 is:
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < apply IH to H3 H4.
Subgoal 2:

Variables: P2 R Q1 C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H3 : at C1 P2 Q1 *
H4 : at C1 P2 Q1
============================
 P2 = P2

Subgoal 3 is:
 P1 = P2

Subgoal 4 is:
 P1 = P2

Subgoal 5 is:
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < search.
Subgoal 3:

Variables: P1 P2 Q1 R C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H2 : at (plus_r R C1) P2 (plus R Q1)
H3 : at C1 P1 Q1 *
============================
 P1 = P2

Subgoal 4 is:
 P1 = P2

Subgoal 5 is:
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < case H2.
Subgoal 3:

Variables: P1 P2 Q1 R C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H3 : at C1 P1 Q1 *
H4 : at C1 P2 Q1
============================
 P1 = P2

Subgoal 4 is:
 P1 = P2

Subgoal 5 is:
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < apply IH to H3 H4.
Subgoal 3:

Variables: P2 Q1 R C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H3 : at C1 P2 Q1 *
H4 : at C1 P2 Q1
============================
 P2 = P2

Subgoal 4 is:
 P1 = P2

Subgoal 5 is:
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < search.
Subgoal 4:

Variables: P1 P2 R Q1 C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H2 : at (par_l C1 R) P2 (par Q1 R)
H3 : at C1 P1 Q1 *
============================
 P1 = P2

Subgoal 5 is:
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < case H2.
Subgoal 4:

Variables: P1 P2 R Q1 C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H3 : at C1 P1 Q1 *
H4 : at C1 P2 Q1
============================
 P1 = P2

Subgoal 5 is:
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < apply IH to H3 H4.
Subgoal 4:

Variables: P2 R Q1 C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H3 : at C1 P2 Q1 *
H4 : at C1 P2 Q1
============================
 P2 = P2

Subgoal 5 is:
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < search.
Subgoal 5:

Variables: P1 P2 Q1 R C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H2 : at (par_r R C1) P2 (par R Q1)
H3 : at C1 P1 Q1 *
============================
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < case H2.
Subgoal 5:

Variables: P1 P2 Q1 R C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H3 : at C1 P1 Q1 *
H4 : at C1 P2 Q1
============================
 P1 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < apply IH to H3 H4.
Subgoal 5:

Variables: P2 Q1 R C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H3 : at C1 P2 Q1 *
H4 : at C1 P2 Q1
============================
 P2 = P2

Subgoal 6 is:
 P1 = P2

at_det2 < search.
Subgoal 6:

Variables: P1 P2 Q1 A C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H2 : at (act_d A C1) P2 (act A Q1)
H3 : at C1 P1 Q1 *
============================
 P1 = P2

at_det2 < case H2.
Subgoal 6:

Variables: P1 P2 Q1 A C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H3 : at C1 P1 Q1 *
H4 : at C1 P2 Q1
============================
 P1 = P2

at_det2 < apply IH to H3 H4.
Subgoal 6:

Variables: P2 Q1 A C1
IH : forall C P1 P2 Q, at C P1 Q * -> at C P2 Q -> P1 = P2
H3 : at C1 P2 Q1 *
H4 : at C1 P2 Q1
============================
 P2 = P2

at_det2 < search.
Proof completed.
Abella < Theorem concat_ctx : 
forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 -> (exists C3, at C3 P1 P3).


============================
 forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 ->
   (exists C3, at C3 P1 P3)

concat_ctx < induction on 2.

IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
============================
 forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 @ ->
   (exists C3, at C3 P1 P3)

concat_ctx < intros.

Variables: C1 P1 C2 P2 P3
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P2
H2 : at C2 P2 P3 @
============================
 exists C3, at C3 P1 P3

concat_ctx < case H2.
Subgoal 1:

Variables: C1 P1 P3
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P3
============================
 exists C3, at C3 P1 P3

Subgoal 2 is:
 exists C3, at C3 P1 (plus Q R)

Subgoal 3 is:
 exists C3, at C3 P1 (plus R Q)

Subgoal 4 is:
 exists C3, at C3 P1 (par Q R)

Subgoal 5 is:
 exists C3, at C3 P1 (par R Q)

Subgoal 6 is:
 exists C3, at C3 P1 (act A Q)

concat_ctx < search.
Subgoal 2:

Variables: C1 P1 P2 R Q C
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P2
H3 : at C P2 Q *
============================
 exists C3, at C3 P1 (plus Q R)

Subgoal 3 is:
 exists C3, at C3 P1 (plus R Q)

Subgoal 4 is:
 exists C3, at C3 P1 (par Q R)

Subgoal 5 is:
 exists C3, at C3 P1 (par R Q)

Subgoal 6 is:
 exists C3, at C3 P1 (act A Q)

concat_ctx < apply IH to H1 H3.
Subgoal 2:

Variables: C1 P1 P2 R Q C C3
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P2
H3 : at C P2 Q *
H4 : at C3 P1 Q
============================
 exists C3, at C3 P1 (plus Q R)

Subgoal 3 is:
 exists C3, at C3 P1 (plus R Q)

Subgoal 4 is:
 exists C3, at C3 P1 (par Q R)

Subgoal 5 is:
 exists C3, at C3 P1 (par R Q)

Subgoal 6 is:
 exists C3, at C3 P1 (act A Q)

concat_ctx < search.
Subgoal 3:

Variables: C1 P1 P2 Q R C
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P2
H3 : at C P2 Q *
============================
 exists C3, at C3 P1 (plus R Q)

Subgoal 4 is:
 exists C3, at C3 P1 (par Q R)

Subgoal 5 is:
 exists C3, at C3 P1 (par R Q)

Subgoal 6 is:
 exists C3, at C3 P1 (act A Q)

concat_ctx < apply IH to H1 H3.
Subgoal 3:

Variables: C1 P1 P2 Q R C C3
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P2
H3 : at C P2 Q *
H4 : at C3 P1 Q
============================
 exists C3, at C3 P1 (plus R Q)

Subgoal 4 is:
 exists C3, at C3 P1 (par Q R)

Subgoal 5 is:
 exists C3, at C3 P1 (par R Q)

Subgoal 6 is:
 exists C3, at C3 P1 (act A Q)

concat_ctx < search.
Subgoal 4:

Variables: C1 P1 P2 R Q C
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P2
H3 : at C P2 Q *
============================
 exists C3, at C3 P1 (par Q R)

Subgoal 5 is:
 exists C3, at C3 P1 (par R Q)

Subgoal 6 is:
 exists C3, at C3 P1 (act A Q)

concat_ctx < apply IH to H1 H3.
Subgoal 4:

Variables: C1 P1 P2 R Q C C3
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P2
H3 : at C P2 Q *
H4 : at C3 P1 Q
============================
 exists C3, at C3 P1 (par Q R)

Subgoal 5 is:
 exists C3, at C3 P1 (par R Q)

Subgoal 6 is:
 exists C3, at C3 P1 (act A Q)

concat_ctx < search.
Subgoal 5:

Variables: C1 P1 P2 Q R C
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P2
H3 : at C P2 Q *
============================
 exists C3, at C3 P1 (par R Q)

Subgoal 6 is:
 exists C3, at C3 P1 (act A Q)

concat_ctx < apply IH to H1 H3.
Subgoal 5:

Variables: C1 P1 P2 Q R C C3
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P2
H3 : at C P2 Q *
H4 : at C3 P1 Q
============================
 exists C3, at C3 P1 (par R Q)

Subgoal 6 is:
 exists C3, at C3 P1 (act A Q)

concat_ctx < search.
Subgoal 6:

Variables: C1 P1 P2 Q A C
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P2
H3 : at C P2 Q *
============================
 exists C3, at C3 P1 (act A Q)

concat_ctx < apply IH to H1 H3.
Subgoal 6:

Variables: C1 P1 P2 Q A C C3
IH : forall C1 P1 C2 P2 P3, at C1 P1 P2 -> at C2 P2 P3 * ->
       (exists C3, at C3 P1 P3)
H1 : at C1 P1 P2
H3 : at C P2 Q *
H4 : at C3 P1 Q
============================
 exists C3, at C3 P1 (act A Q)

concat_ctx < search.
Proof completed.
Abella < Theorem ctx_faithful : 
forall C P P0 A R, at C P P0 -> one P0 A R ->
  (exists CC, at CC P R /\
       (forall Q Q0, at C Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR))) \/
  (exists CC PBP B, one P B PBP /\ at CC PBP R /\
       (forall Q QBQ, one Q B QBQ ->
            (forall Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
  (forall Q Q0, at C Q Q0 -> one Q0 A R).


============================
 forall C P P0 A R, at C P P0 -> one P0 A R ->
   (exists CC, at CC P R /\
        (forall Q Q0, at C Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at C Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at C Q Q0 -> one Q0 A R)

ctx_faithful < induction on 1.

IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
============================
 forall C P P0 A R, at C P P0 @ -> one P0 A R ->
   (exists CC, at CC P R /\
        (forall Q Q0, at C Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at C Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at C Q Q0 -> one Q0 A R)

ctx_faithful < intros.

Variables: C P P0 A R
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at C P P0 @
H2 : one P0 A R
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at C Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at C Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at C Q Q0 -> one Q0 A R)

ctx_faithful < case H1 (keep).
Subgoal 1:

Variables: P0 A R
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
============================
 (exists CC, at CC P0 R /\
      (forall Q Q0, at hole Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P0 B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at hole Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at hole Q Q0 -> one Q0 A R)

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 1:

Variables: P0 A R
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
============================
 (exists CC, at CC P0 R /\
      (forall Q Q0, at hole Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P0 B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at hole Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 1:

Variables: P0 A R
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
============================
 exists CC PBP B, one P0 B PBP /\ at CC PBP R /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at hole Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)))

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness hole.
Subgoal 1:

Variables: P0 A R
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
============================
 exists PBP B, one P0 B PBP /\ at hole PBP R /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at hole Q Q0 ->
             (exists RR, one Q0 A RR /\ at hole QBQ RR)))

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness R.
Subgoal 1:

Variables: P0 A R
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
============================
 exists B, one P0 B R /\ at hole R R /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at hole Q Q0 ->
             (exists RR, one Q0 A RR /\ at hole QBQ RR)))

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness A.
Subgoal 1:

Variables: P0 A R
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
============================
 one P0 A R /\ at hole R R /\
   (forall Q QBQ, one Q A QBQ ->
        (forall Q0, at hole Q Q0 ->
             (exists RR, one Q0 A RR /\ at hole QBQ RR)))

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 1.1:

Variables: P0 A R
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
============================
 one P0 A R

Subgoal 1.2 is:
 at hole R R

Subgoal 1.3 is:
 forall Q QBQ, one Q A QBQ ->
   (forall Q0, at hole Q Q0 -> (exists RR, one Q0 A RR /\ at hole QBQ RR))

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 1.2:

Variables: P0 A R
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
============================
 at hole R R

Subgoal 1.3 is:
 forall Q QBQ, one Q A QBQ ->
   (forall Q0, at hole Q Q0 -> (exists RR, one Q0 A RR /\ at hole QBQ RR))

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 1.3:

Variables: P0 A R
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
============================
 forall Q QBQ, one Q A QBQ ->
   (forall Q0, at hole Q Q0 -> (exists RR, one Q0 A RR /\ at hole QBQ RR))

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 1.3:

Variables: P0 A R Q QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
H3 : one Q A QBQ
H4 : at hole Q Q0
============================
 exists RR, one Q0 A RR /\ at hole QBQ RR

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H4.
Subgoal 1.3:

Variables: P0 A R QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
H3 : one Q0 A QBQ
============================
 exists RR, one Q0 A RR /\ at hole QBQ RR

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness QBQ.
Subgoal 1.3:

Variables: P0 A R QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at hole P0 P0 @
H2 : one P0 A R
H3 : one Q0 A QBQ
============================
 one Q0 A QBQ /\ at hole QBQ QBQ

Subgoal 2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 2:

Variables: P A R R1 Q C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H2 : one (plus Q R1) A R
H3 : at C1 P Q *
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H2.
Subgoal 2.1:

Variables: P A R R1 Q C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply IH to H3 H4.
Subgoal 2.1:

Variables: P A R R1 Q C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H5 : (exists CC, at CC P R /\
          (forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C1 Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C1 Q Q0 -> one Q0 A R)
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H5.
Subgoal 2.1.1:

Variables: P A R R1 Q C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.1.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 2.1.1:

Variables: P A R R1 Q C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

Subgoal 2.1.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 2.1.1:

Variables: P A R R1 Q C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 exists CC, at CC P R /\
   (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC Q RR))

Subgoal 2.1.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness CC.
Subgoal 2.1.1:

Variables: P A R R1 Q C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 at CC P R /\
   (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC Q RR))

Subgoal 2.1.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 2.1.1.1:

Variables: P A R R1 Q C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 at CC P R

Subgoal 2.1.1.2 is:
 forall Q Q0, at (plus_l C1 R1) Q Q0 ->
   (exists RR, one Q0 A RR /\ at CC Q RR)

Subgoal 2.1.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 2.1.1.2:

Variables: P A R R1 Q C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 forall Q Q0, at (plus_l C1 R1) Q Q0 ->
   (exists RR, one Q0 A RR /\ at CC Q RR)

Subgoal 2.1.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 2.1.1.2:

Variables: P A R R1 Q C1 CC Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H8 : at (plus_l C1 R1) Q1 Q0
============================
 exists RR, one Q0 A RR /\ at CC Q1 RR

Subgoal 2.1.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H8.
Subgoal 2.1.1.2:

Variables: P A R R1 Q C1 CC Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H9 : at C1 Q1 Q2
============================
 exists RR, one (plus Q2 R1) A RR /\ at CC Q1 RR

Subgoal 2.1.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H7 to H9.
Subgoal 2.1.1.2:

Variables: P A R R1 Q C1 CC Q1 Q2 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H9 : at C1 Q1 Q2
H10 : one Q2 A RR
H11 : at CC Q1 RR
============================
 exists RR, one (plus Q2 R1) A RR /\ at CC Q1 RR

Subgoal 2.1.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 2.1.2:

Variables: P A R R1 Q C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 2.1.2:

Variables: P A R R1 Q C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 2.1.2:

Variables: P A R R1 Q C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists CC PBP B, one P B PBP /\ at CC PBP R /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (plus_l C1 R1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at CC QBQ RR)))

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness CC.
Subgoal 2.1.2:

Variables: P A R R1 Q C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists PBP B, one P B PBP /\ at CC PBP R /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (plus_l C1 R1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at CC QBQ RR)))

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness PBP.
Subgoal 2.1.2:

Variables: P A R R1 Q C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists B, one P B PBP /\ at CC PBP R /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (plus_l C1 R1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at CC QBQ RR)))

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness B.
Subgoal 2.1.2:

Variables: P A R R1 Q C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 one P B PBP /\ at CC PBP R /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (plus_l C1 R1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at CC QBQ RR)))

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 2.1.2.1:

Variables: P A R R1 Q C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 one P B PBP

Subgoal 2.1.2.2 is:
 at CC PBP R

Subgoal 2.1.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (plus_l C1 R1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC QBQ RR))

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 2.1.2.2:

Variables: P A R R1 Q C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 at CC PBP R

Subgoal 2.1.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (plus_l C1 R1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC QBQ RR))

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 2.1.2.3:

Variables: P A R R1 Q C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (plus_l C1 R1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC QBQ RR))

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 2.1.2.3:

Variables: P A R R1 Q C1 CC PBP B Q1 QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H10 : at (plus_l C1 R1) Q1 Q0
============================
 exists RR, one Q0 A RR /\ at CC QBQ RR

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H8 to H9.
Subgoal 2.1.2.3:

Variables: P A R R1 Q C1 CC PBP B Q1 QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H10 : at (plus_l C1 R1) Q1 Q0
H11 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)
============================
 exists RR, one Q0 A RR /\ at CC QBQ RR

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H10.
Subgoal 2.1.2.3:

Variables: P A R R1 Q C1 CC PBP B Q1 QBQ Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H11 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)
H12 : at C1 Q1 Q2
============================
 exists RR, one (plus Q2 R1) A RR /\ at CC QBQ RR

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H11 to H12.
Subgoal 2.1.2.3:

Variables: P A R R1 Q C1 CC PBP B Q1 QBQ Q2 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H11 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)
H12 : at C1 Q1 Q2
H13 : one Q2 A RR
H14 : at CC QBQ RR
============================
 exists RR, one (plus Q2 R1) A RR /\ at CC QBQ RR

Subgoal 2.1.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 2.1.3:

Variables: P A R R1 Q C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A R
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 2.1.3:

Variables: P A R R1 Q C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A R
============================
 forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 2.1.3:

Variables: P A R R1 Q C1 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A R
H7 : at (plus_l C1 R1) Q1 Q0
============================
 one Q0 A R

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H7.
Subgoal 2.1.3:

Variables: P A R R1 Q C1 Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A R
H8 : at C1 Q1 Q2
============================
 one (plus Q2 R1) A R

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H6 to H8.
Subgoal 2.1.3:

Variables: P A R R1 Q C1 Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A R
H8 : at C1 Q1 Q2
H9 : one Q2 A R
============================
 one (plus Q2 R1) A R

Subgoal 2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 2.2:

Variables: P A R R1 Q C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one R1 A R
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 2.2:

Variables: P A R R1 Q C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one R1 A R
============================
 forall Q Q0, at (plus_l C1 R1) Q Q0 -> one Q0 A R

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 2.2:

Variables: P A R R1 Q C1 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one R1 A R
H5 : at (plus_l C1 R1) Q1 Q0
============================
 one Q0 A R

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H5.
Subgoal 2.2:

Variables: P A R R1 Q C1 Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_l C1 R1) P (plus Q R1) @
H3 : at C1 P Q *
H4 : one R1 A R
H6 : at C1 Q1 Q2
============================
 one (plus Q2 R1) A R

Subgoal 3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 3:

Variables: P A R Q R1 C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H2 : one (plus R1 Q) A R
H3 : at C1 P Q *
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H2.
Subgoal 3.1:

Variables: P A R Q R1 C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A R
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 3.1:

Variables: P A R Q R1 C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A R
============================
 forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R

Subgoal 3.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 3.1:

Variables: P A R Q R1 C1 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A R
H5 : at (plus_r R1 C1) Q1 Q0
============================
 one Q0 A R

Subgoal 3.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H5.
Subgoal 3.1:

Variables: P A R Q R1 C1 Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A R
H6 : at C1 Q1 Q2
============================
 one (plus R1 Q2) A R

Subgoal 3.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 3.2:

Variables: P A R Q R1 C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply IH to H3 H4.
Subgoal 3.2:

Variables: P A R Q R1 C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H5 : (exists CC, at CC P R /\
          (forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C1 Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C1 Q Q0 -> one Q0 A R)
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H5.
Subgoal 3.2.1:

Variables: P A R Q R1 C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 3.2.1:

Variables: P A R Q R1 C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

Subgoal 3.2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 3.2.1:

Variables: P A R Q R1 C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 exists CC, at CC P R /\
   (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC Q RR))

Subgoal 3.2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness CC.
Subgoal 3.2.1:

Variables: P A R Q R1 C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 at CC P R /\
   (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC Q RR))

Subgoal 3.2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 3.2.1.1:

Variables: P A R Q R1 C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 at CC P R

Subgoal 3.2.1.2 is:
 forall Q Q0, at (plus_r R1 C1) Q Q0 ->
   (exists RR, one Q0 A RR /\ at CC Q RR)

Subgoal 3.2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 3.2.1.2:

Variables: P A R Q R1 C1 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 forall Q Q0, at (plus_r R1 C1) Q Q0 ->
   (exists RR, one Q0 A RR /\ at CC Q RR)

Subgoal 3.2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 3.2.1.2:

Variables: P A R Q R1 C1 CC Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H8 : at (plus_r R1 C1) Q1 Q0
============================
 exists RR, one Q0 A RR /\ at CC Q1 RR

Subgoal 3.2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H8.
Subgoal 3.2.1.2:

Variables: P A R Q R1 C1 CC Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H9 : at C1 Q1 Q2
============================
 exists RR, one (plus R1 Q2) A RR /\ at CC Q1 RR

Subgoal 3.2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H7 to H9.
Subgoal 3.2.1.2:

Variables: P A R Q R1 C1 CC Q1 Q2 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : at CC P R
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H9 : at C1 Q1 Q2
H10 : one Q2 A RR
H11 : at CC Q1 RR
============================
 exists RR, one (plus R1 Q2) A RR /\ at CC Q1 RR

Subgoal 3.2.2 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 3.2.2:

Variables: P A R Q R1 C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 3.2.2:

Variables: P A R Q R1 C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 3.2.2:

Variables: P A R Q R1 C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists CC PBP B, one P B PBP /\ at CC PBP R /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (plus_r R1 C1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at CC QBQ RR)))

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness CC.
Subgoal 3.2.2:

Variables: P A R Q R1 C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists PBP B, one P B PBP /\ at CC PBP R /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (plus_r R1 C1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at CC QBQ RR)))

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness PBP.
Subgoal 3.2.2:

Variables: P A R Q R1 C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists B, one P B PBP /\ at CC PBP R /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (plus_r R1 C1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at CC QBQ RR)))

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness B.
Subgoal 3.2.2:

Variables: P A R Q R1 C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 one P B PBP /\ at CC PBP R /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (plus_r R1 C1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at CC QBQ RR)))

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 3.2.2.1:

Variables: P A R Q R1 C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 one P B PBP

Subgoal 3.2.2.2 is:
 at CC PBP R

Subgoal 3.2.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (plus_r R1 C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC QBQ RR))

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 3.2.2.2:

Variables: P A R Q R1 C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 at CC PBP R

Subgoal 3.2.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (plus_r R1 C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC QBQ RR))

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 3.2.2.3:

Variables: P A R Q R1 C1 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (plus_r R1 C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC QBQ RR))

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 3.2.2.3:

Variables: P A R Q R1 C1 CC PBP B Q1 QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H10 : at (plus_r R1 C1) Q1 Q0
============================
 exists RR, one Q0 A RR /\ at CC QBQ RR

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H8 to H9.
Subgoal 3.2.2.3:

Variables: P A R Q R1 C1 CC PBP B Q1 QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H10 : at (plus_r R1 C1) Q1 Q0
H11 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)
============================
 exists RR, one Q0 A RR /\ at CC QBQ RR

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H10.
Subgoal 3.2.2.3:

Variables: P A R Q R1 C1 CC PBP B Q1 QBQ Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H11 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)
H12 : at C1 Q1 Q2
============================
 exists RR, one (plus R1 Q2) A RR /\ at CC QBQ RR

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H11 to H12.
Subgoal 3.2.2.3:

Variables: P A R Q R1 C1 CC PBP B Q1 QBQ Q2 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : one P B PBP
H7 : at CC PBP R
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H11 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)
H12 : at C1 Q1 Q2
H13 : one Q2 A RR
H14 : at CC QBQ RR
============================
 exists RR, one (plus R1 Q2) A RR /\ at CC QBQ RR

Subgoal 3.2.3 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 3.2.3:

Variables: P A R Q R1 C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A R
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (plus_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (plus_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 3.2.3:

Variables: P A R Q R1 C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A R
============================
 forall Q Q0, at (plus_r R1 C1) Q Q0 -> one Q0 A R

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 3.2.3:

Variables: P A R Q R1 C1 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A R
H7 : at (plus_r R1 C1) Q1 Q0
============================
 one Q0 A R

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H7.
Subgoal 3.2.3:

Variables: P A R Q R1 C1 Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A R
H8 : at C1 Q1 Q2
============================
 one (plus R1 Q2) A R

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H6 to H8.
Subgoal 3.2.3:

Variables: P A R Q R1 C1 Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (plus_r R1 C1) P (plus R1 Q) @
H3 : at C1 P Q *
H4 : one Q A R
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A R
H8 : at C1 Q1 Q2
H9 : one Q2 A R
============================
 one (plus R1 Q2) A R

Subgoal 4 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4:

Variables: P A R R1 Q C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H2 : one (par Q R1) A R
H3 : at C1 P Q *
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A R)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H2.
Subgoal 4.1:

Variables: P A R1 Q C1 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
============================
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply IH to H3 H4.
Subgoal 4.1:

Variables: P A R1 Q C1 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H5 : (exists CC, at CC P P2 /\
          (forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP P2 /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C1 Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C1 Q Q0 -> one Q0 A P2)
============================
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H5.
Subgoal 4.1.1:

Variables: P A R1 Q C1 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : at CC P P2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.2 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 4.1.1:

Variables: P A R1 Q C1 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : at CC P P2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

Subgoal 4.1.2 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 4.1.1:

Variables: P A R1 Q C1 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : at CC P P2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 exists CC, at CC P (par P2 R1) /\
   (forall Q Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC Q RR))

Subgoal 4.1.2 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_l CC R1.
Subgoal 4.1.1:

Variables: P A R1 Q C1 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : at CC P P2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 at (par_l CC R1) P (par P2 R1) /\
   (forall Q Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at (par_l CC R1) Q RR))

Subgoal 4.1.2 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 4.1.1.1:

Variables: P A R1 Q C1 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : at CC P P2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 at (par_l CC R1) P (par P2 R1)

Subgoal 4.1.1.2 is:
 forall Q Q0, at (par_l C1 R1) Q Q0 ->
   (exists RR, one Q0 A RR /\ at (par_l CC R1) Q RR)

Subgoal 4.1.2 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.1.1.2:

Variables: P A R1 Q C1 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : at CC P P2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 forall Q Q0, at (par_l C1 R1) Q Q0 ->
   (exists RR, one Q0 A RR /\ at (par_l CC R1) Q RR)

Subgoal 4.1.2 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 4.1.1.2:

Variables: P A R1 Q C1 P2 CC Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : at CC P P2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H8 : at (par_l C1 R1) Q1 Q0
============================
 exists RR, one Q0 A RR /\ at (par_l CC R1) Q1 RR

Subgoal 4.1.2 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H8.
Subgoal 4.1.1.2:

Variables: P A R1 Q C1 P2 CC Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : at CC P P2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H9 : at C1 Q1 Q2
============================
 exists RR, one (par Q2 R1) A RR /\ at (par_l CC R1) Q1 RR

Subgoal 4.1.2 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H7 to H9.
Subgoal 4.1.1.2:

Variables: P A R1 Q C1 P2 CC Q1 Q2 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : at CC P P2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H9 : at C1 Q1 Q2
H10 : one Q2 A RR
H11 : at CC Q1 RR
============================
 exists RR, one (par Q2 R1) A RR /\ at (par_l CC R1) Q1 RR

Subgoal 4.1.2 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par RR R1.
Subgoal 4.1.1.2:

Variables: P A R1 Q C1 P2 CC Q1 Q2 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : at CC P P2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H9 : at C1 Q1 Q2
H10 : one Q2 A RR
H11 : at CC Q1 RR
============================
 one (par Q2 R1) A (par RR R1) /\ at (par_l CC R1) Q1 (par RR R1)

Subgoal 4.1.2 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.1.2:

Variables: P A R1 Q C1 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 4.1.2:

Variables: P A R1 Q C1 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 4.1.2:

Variables: P A R1 Q C1 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at CC QBQ RR)))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_l CC R1.
Subgoal 4.1.2:

Variables: P A R1 Q C1 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists PBP B, one P B PBP /\ at (par_l CC R1) PBP (par P2 R1) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at (par_l CC R1) QBQ RR)))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness PBP.
Subgoal 4.1.2:

Variables: P A R1 Q C1 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists B, one P B PBP /\ at (par_l CC R1) PBP (par P2 R1) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at (par_l CC R1) QBQ RR)))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness B.
Subgoal 4.1.2:

Variables: P A R1 Q C1 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 one P B PBP /\ at (par_l CC R1) PBP (par P2 R1) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at (par_l CC R1) QBQ RR)))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 4.1.2.1:

Variables: P A R1 Q C1 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 one P B PBP

Subgoal 4.1.2.2 is:
 at (par_l CC R1) PBP (par P2 R1)

Subgoal 4.1.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at (par_l CC R1) QBQ RR))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.1.2.2:

Variables: P A R1 Q C1 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 at (par_l CC R1) PBP (par P2 R1)

Subgoal 4.1.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at (par_l CC R1) QBQ RR))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.1.2.3:

Variables: P A R1 Q C1 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at (par_l CC R1) QBQ RR))

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 4.1.2.3:

Variables: P A R1 Q C1 P2 CC PBP B Q1 QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H10 : at (par_l C1 R1) Q1 Q0
============================
 exists RR, one Q0 A RR /\ at (par_l CC R1) QBQ RR

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H10.
Subgoal 4.1.2.3:

Variables: P A R1 Q C1 P2 CC PBP B Q1 QBQ Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H11 : at C1 Q1 Q2
============================
 exists RR, one (par Q2 R1) A RR /\ at (par_l CC R1) QBQ RR

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H8 to H9.
Subgoal 4.1.2.3:

Variables: P A R1 Q C1 P2 CC PBP B Q1 QBQ Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H11 : at C1 Q1 Q2
H12 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)
============================
 exists RR, one (par Q2 R1) A RR /\ at (par_l CC R1) QBQ RR

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H12 to H11.
Subgoal 4.1.2.3:

Variables: P A R1 Q C1 P2 CC PBP B Q1 QBQ Q2 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H11 : at C1 Q1 Q2
H12 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)
H13 : one Q2 A RR
H14 : at CC QBQ RR
============================
 exists RR, one (par Q2 R1) A RR /\ at (par_l CC R1) QBQ RR

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par RR R1.
Subgoal 4.1.2.3:

Variables: P A R1 Q C1 P2 CC PBP B Q1 QBQ Q2 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : one P B PBP
H7 : at CC PBP P2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H11 : at C1 Q1 Q2
H12 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)
H13 : one Q2 A RR
H14 : at CC QBQ RR
============================
 one (par Q2 R1) A (par RR R1) /\ at (par_l CC R1) QBQ (par RR R1)

Subgoal 4.1.3 is:
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.1.3:

Variables: P A R1 Q C1 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A P2
============================
 (exists CC, at CC P (par P2 R1) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 R1) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1))

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 4.1.3:

Variables: P A R1 Q C1 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A P2
============================
 forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 A (par P2 R1)

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 4.1.3:

Variables: P A R1 Q C1 P2 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A P2
H7 : at (par_l C1 R1) Q1 Q0
============================
 one Q0 A (par P2 R1)

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H7.
Subgoal 4.1.3:

Variables: P A R1 Q C1 P2 Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A P2
H8 : at C1 Q1 Q2
============================
 one (par Q2 R1) A (par P2 R1)

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H6 to H8.
Subgoal 4.1.3:

Variables: P A R1 Q C1 P2 Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q A P2
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A P2
H8 : at C1 Q1 Q2
H9 : one Q2 A P2
============================
 one (par Q2 R1) A (par P2 R1)

Subgoal 4.2 is:
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.2:

Variables: P A R1 Q C1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one R1 A Q2
============================
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 -> one Q0 A (par Q Q2))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 4.2:

Variables: P A R1 Q C1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one R1 A Q2
============================
 (exists CC, at CC P (par Q Q2) /\
      (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par Q Q2) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_l C1 R1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 4.2:

Variables: P A R1 Q C1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one R1 A Q2
============================
 exists CC, at CC P (par Q Q2) /\
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
        (exists RR, one Q0 A RR /\ at CC Q1 RR))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_l C1 Q2.
Subgoal 4.2:

Variables: P A R1 Q C1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one R1 A Q2
============================
 at (par_l C1 Q2) P (par Q Q2) /\
   (forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
        (exists RR, one Q0 A RR /\ at (par_l C1 Q2) Q1 RR))

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 4.2.1:

Variables: P A R1 Q C1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one R1 A Q2
============================
 at (par_l C1 Q2) P (par Q Q2)

Subgoal 4.2.2 is:
 forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
   (exists RR, one Q0 A RR /\ at (par_l C1 Q2) Q1 RR)

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.2.2:

Variables: P A R1 Q C1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one R1 A Q2
============================
 forall Q1 Q0, at (par_l C1 R1) Q1 Q0 ->
   (exists RR, one Q0 A RR /\ at (par_l C1 Q2) Q1 RR)

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 4.2.2:

Variables: P A R1 Q C1 Q2 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one R1 A Q2
H5 : at (par_l C1 R1) Q1 Q0
============================
 exists RR, one Q0 A RR /\ at (par_l C1 Q2) Q1 RR

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H5.
Subgoal 4.2.2:

Variables: P A R1 Q C1 Q2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one R1 A Q2
H6 : at C1 Q1 Q3
============================
 exists RR, one (par Q3 R1) A RR /\ at (par_l C1 Q2) Q1 RR

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par Q3 Q2.
Subgoal 4.2.2:

Variables: P A R1 Q C1 Q2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one R1 A Q2
H6 : at C1 Q1 Q3
============================
 one (par Q3 R1) A (par Q3 Q2) /\ at (par_l C1 Q2) Q1 (par Q3 Q2)

Subgoal 4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.3:

Variables: P R1 Q C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply IH to H3 H4.
Subgoal 4.3:

Variables: P R1 Q C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H6 : (exists CC, at CC P P2 /\
          (forall Q Q0, at C1 Q Q0 ->
               (exists RR, one Q0 (up X) RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP P2 /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C1 Q Q0 ->
                      (exists RR, one Q0 (up X) RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C1 Q Q0 -> one Q0 (up X) P2)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H6.
Subgoal 4.3.1:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 4.3.1:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR))))

Subgoal 4.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 4.3.1:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 exists CC, at CC P (par P2 Q2) /\
   (forall Q Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at CC Q RR))

Subgoal 4.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_l CC Q2.
Subgoal 4.3.1:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 at (par_l CC Q2) P (par P2 Q2) /\
   (forall Q Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_l CC Q2) Q RR))

Subgoal 4.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 4.3.1.1:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 at (par_l CC Q2) P (par P2 Q2)

Subgoal 4.3.1.2 is:
 forall Q Q0, at (par_l C1 R1) Q Q0 ->
   (exists RR, one Q0 tau RR /\ at (par_l CC Q2) Q RR)

Subgoal 4.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.3.1.2:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 forall Q Q0, at (par_l C1 R1) Q Q0 ->
   (exists RR, one Q0 tau RR /\ at (par_l CC Q2) Q RR)

Subgoal 4.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 4.3.1.2:

Variables: P R1 Q C1 X Q2 P2 CC Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
H9 : at (par_l C1 R1) Q1 Q0
============================
 exists RR, one Q0 tau RR /\ at (par_l CC Q2) Q1 RR

Subgoal 4.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H9.
Subgoal 4.3.1.2:

Variables: P R1 Q C1 X Q2 P2 CC Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
H10 : at C1 Q1 Q3
============================
 exists RR, one (par Q3 R1) tau RR /\ at (par_l CC Q2) Q1 RR

Subgoal 4.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H8 to H10.
Subgoal 4.3.1.2:

Variables: P R1 Q C1 X Q2 P2 CC Q1 Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
H10 : at C1 Q1 Q3
H11 : one Q3 (up X) RR
H12 : at CC Q1 RR
============================
 exists RR, one (par Q3 R1) tau RR /\ at (par_l CC Q2) Q1 RR

Subgoal 4.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par RR Q2.
Subgoal 4.3.1.2:

Variables: P R1 Q C1 X Q2 P2 CC Q1 Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
H10 : at C1 Q1 Q3
H11 : one Q3 (up X) RR
H12 : at CC Q1 RR
============================
 one (par Q3 R1) tau (par RR Q2) /\ at (par_l CC Q2) Q1 (par RR Q2)

Subgoal 4.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.3.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 4.3.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR))))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 4.3.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at CC QBQ RR)))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_l CC Q2.
Subgoal 4.3.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 exists PBP B, one P B PBP /\ at (par_l CC Q2) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR)))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness PBP.
Subgoal 4.3.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 exists B, one P B PBP /\ at (par_l CC Q2) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR)))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness B.
Subgoal 4.3.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 one P B PBP /\ at (par_l CC Q2) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR)))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 4.3.2.1:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 one P B PBP

Subgoal 4.3.2.2 is:
 at (par_l CC Q2) PBP (par P2 Q2)

Subgoal 4.3.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.3.2.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 at (par_l CC Q2) PBP (par P2 Q2)

Subgoal 4.3.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.3.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR))

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 4.3.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B Q1 QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H11 : at (par_l C1 R1) Q1 Q0
============================
 exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H11.
Subgoal 4.3.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B Q1 QBQ Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
============================
 exists RR, one (par Q3 R1) tau RR /\ at (par_l CC Q2) QBQ RR

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H9 to H10.
Subgoal 4.3.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B Q1 QBQ Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
H13 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 (up X) RR /\ at CC QBQ RR)
============================
 exists RR, one (par Q3 R1) tau RR /\ at (par_l CC Q2) QBQ RR

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H13 to H12.
Subgoal 4.3.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B Q1 QBQ Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
H13 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 (up X) RR /\ at CC QBQ RR)
H14 : one Q3 (up X) RR
H15 : at CC QBQ RR
============================
 exists RR, one (par Q3 R1) tau RR /\ at (par_l CC Q2) QBQ RR

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par RR Q2.
Subgoal 4.3.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B Q1 QBQ Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
H13 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 (up X) RR /\ at CC QBQ RR)
H14 : one Q3 (up X) RR
H15 : at CC QBQ RR
============================
 one (par Q3 R1) tau (par RR Q2) /\ at (par_l CC Q2) QBQ (par RR Q2)

Subgoal 4.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.3.3:

Variables: P R1 Q C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (up X) P2
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 4.3.3:

Variables: P R1 Q C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (up X) P2
============================
 forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2)

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 4.3.3:

Variables: P R1 Q C1 X Q2 P2 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (up X) P2
H8 : at (par_l C1 R1) Q1 Q0
============================
 one Q0 tau (par P2 Q2)

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H8.
Subgoal 4.3.3:

Variables: P R1 Q C1 X Q2 P2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (up X) P2
H9 : at C1 Q1 Q3
============================
 one (par Q3 R1) tau (par P2 Q2)

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H7 to H9.
Subgoal 4.3.3:

Variables: P R1 Q C1 X Q2 P2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (up X) P2
H5 : one R1 (dn X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (up X) P2
H9 : at C1 Q1 Q3
H10 : one Q3 (up X) P2
============================
 one (par Q3 R1) tau (par P2 Q2)

Subgoal 4.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.4:

Variables: P R1 Q C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply IH to H3 H4.
Subgoal 4.4:

Variables: P R1 Q C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H6 : (exists CC, at CC P P2 /\
          (forall Q Q0, at C1 Q Q0 ->
               (exists RR, one Q0 (dn X) RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP P2 /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C1 Q Q0 ->
                      (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) P2)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H6.
Subgoal 4.4.1:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 4.4.1:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR))))

Subgoal 4.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 4.4.1:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 exists CC, at CC P (par P2 Q2) /\
   (forall Q Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at CC Q RR))

Subgoal 4.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_l CC Q2.
Subgoal 4.4.1:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 at (par_l CC Q2) P (par P2 Q2) /\
   (forall Q Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_l CC Q2) Q RR))

Subgoal 4.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 4.4.1.1:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 at (par_l CC Q2) P (par P2 Q2)

Subgoal 4.4.1.2 is:
 forall Q Q0, at (par_l C1 R1) Q Q0 ->
   (exists RR, one Q0 tau RR /\ at (par_l CC Q2) Q RR)

Subgoal 4.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.4.1.2:

Variables: P R1 Q C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 forall Q Q0, at (par_l C1 R1) Q Q0 ->
   (exists RR, one Q0 tau RR /\ at (par_l CC Q2) Q RR)

Subgoal 4.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 4.4.1.2:

Variables: P R1 Q C1 X Q2 P2 CC Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
H9 : at (par_l C1 R1) Q1 Q0
============================
 exists RR, one Q0 tau RR /\ at (par_l CC Q2) Q1 RR

Subgoal 4.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H9.
Subgoal 4.4.1.2:

Variables: P R1 Q C1 X Q2 P2 CC Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
H10 : at C1 Q1 Q3
============================
 exists RR, one (par Q3 R1) tau RR /\ at (par_l CC Q2) Q1 RR

Subgoal 4.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H8 to H10.
Subgoal 4.4.1.2:

Variables: P R1 Q C1 X Q2 P2 CC Q1 Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
H10 : at C1 Q1 Q3
H11 : one Q3 (dn X) RR
H12 : at CC Q1 RR
============================
 exists RR, one (par Q3 R1) tau RR /\ at (par_l CC Q2) Q1 RR

Subgoal 4.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par RR Q2.
Subgoal 4.4.1.2:

Variables: P R1 Q C1 X Q2 P2 CC Q1 Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : at CC P P2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
H10 : at C1 Q1 Q3
H11 : one Q3 (dn X) RR
H12 : at CC Q1 RR
============================
 one (par Q3 R1) tau (par RR Q2) /\ at (par_l CC Q2) Q1 (par RR Q2)

Subgoal 4.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.4.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 4.4.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR))))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 4.4.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at CC QBQ RR)))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_l CC Q2.
Subgoal 4.4.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 exists PBP B, one P B PBP /\ at (par_l CC Q2) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR)))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness PBP.
Subgoal 4.4.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 exists B, one P B PBP /\ at (par_l CC Q2) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR)))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness B.
Subgoal 4.4.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 one P B PBP /\ at (par_l CC Q2) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_l C1 R1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR)))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 4.4.2.1:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 one P B PBP

Subgoal 4.4.2.2 is:
 at (par_l CC Q2) PBP (par P2 Q2)

Subgoal 4.4.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.4.2.2:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 at (par_l CC Q2) PBP (par P2 Q2)

Subgoal 4.4.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.4.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_l C1 R1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR))

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 4.4.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B Q1 QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H11 : at (par_l C1 R1) Q1 Q0
============================
 exists RR, one Q0 tau RR /\ at (par_l CC Q2) QBQ RR

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H11.
Subgoal 4.4.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B Q1 QBQ Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
============================
 exists RR, one (par Q3 R1) tau RR /\ at (par_l CC Q2) QBQ RR

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H9 to H10.
Subgoal 4.4.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B Q1 QBQ Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
H13 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR)
============================
 exists RR, one (par Q3 R1) tau RR /\ at (par_l CC Q2) QBQ RR

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H13 to H12.
Subgoal 4.4.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B Q1 QBQ Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
H13 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR)
H14 : one Q3 (dn X) RR
H15 : at CC QBQ RR
============================
 exists RR, one (par Q3 R1) tau RR /\ at (par_l CC Q2) QBQ RR

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par RR Q2.
Subgoal 4.4.2.3:

Variables: P R1 Q C1 X Q2 P2 CC PBP B Q1 QBQ Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : one P B PBP
H8 : at CC PBP P2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
H13 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR)
H14 : one Q3 (dn X) RR
H15 : at CC QBQ RR
============================
 one (par Q3 R1) tau (par RR Q2) /\ at (par_l CC Q2) QBQ (par RR Q2)

Subgoal 4.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 4.4.3:

Variables: P R1 Q C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) P2
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_l C1 R1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_l C1 R1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 4.4.3:

Variables: P R1 Q C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) P2
============================
 forall Q Q0, at (par_l C1 R1) Q Q0 -> one Q0 tau (par P2 Q2)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 4.4.3:

Variables: P R1 Q C1 X Q2 P2 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) P2
H8 : at (par_l C1 R1) Q1 Q0
============================
 one Q0 tau (par P2 Q2)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H8.
Subgoal 4.4.3:

Variables: P R1 Q C1 X Q2 P2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) P2
H9 : at C1 Q1 Q3
============================
 one (par Q3 R1) tau (par P2 Q2)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H7 to H9.
Subgoal 4.4.3:

Variables: P R1 Q C1 X Q2 P2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_l C1 R1) P (par Q R1) @
H3 : at C1 P Q *
H4 : one Q (dn X) P2
H5 : one R1 (up X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) P2
H9 : at C1 Q1 Q3
H10 : one Q3 (dn X) P2
============================
 one (par Q3 R1) tau (par P2 Q2)

Subgoal 5 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5:

Variables: P A R Q R1 C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H2 : one (par R1 Q) A R
H3 : at C1 P Q *
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A R)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H2.
Subgoal 5.1:

Variables: P A Q R1 C1 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A P2
============================
 (exists CC, at CC P (par P2 Q) /\
      (forall Q1 Q0, at (par_r R1 C1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_r R1 C1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q1 Q0, at (par_r R1 C1) Q1 Q0 -> one Q0 A (par P2 Q))

Subgoal 5.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 5.1:

Variables: P A Q R1 C1 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A P2
============================
 (exists CC, at CC P (par P2 Q) /\
      (forall Q1 Q0, at (par_r R1 C1) Q1 Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q1 RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q) /\
        (forall Q1 QBQ, one Q1 B QBQ ->
             (forall Q0, at (par_r R1 C1) Q1 Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

Subgoal 5.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 5.1:

Variables: P A Q R1 C1 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A P2
============================
 exists CC, at CC P (par P2 Q) /\
   (forall Q1 Q0, at (par_r R1 C1) Q1 Q0 ->
        (exists RR, one Q0 A RR /\ at CC Q1 RR))

Subgoal 5.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_r P2 C1.
Subgoal 5.1:

Variables: P A Q R1 C1 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A P2
============================
 at (par_r P2 C1) P (par P2 Q) /\
   (forall Q1 Q0, at (par_r R1 C1) Q1 Q0 ->
        (exists RR, one Q0 A RR /\ at (par_r P2 C1) Q1 RR))

Subgoal 5.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 5.1.1:

Variables: P A Q R1 C1 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A P2
============================
 at (par_r P2 C1) P (par P2 Q)

Subgoal 5.1.2 is:
 forall Q1 Q0, at (par_r R1 C1) Q1 Q0 ->
   (exists RR, one Q0 A RR /\ at (par_r P2 C1) Q1 RR)

Subgoal 5.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.1.2:

Variables: P A Q R1 C1 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A P2
============================
 forall Q1 Q0, at (par_r R1 C1) Q1 Q0 ->
   (exists RR, one Q0 A RR /\ at (par_r P2 C1) Q1 RR)

Subgoal 5.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 5.1.2:

Variables: P A Q R1 C1 P2 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A P2
H5 : at (par_r R1 C1) Q1 Q0
============================
 exists RR, one Q0 A RR /\ at (par_r P2 C1) Q1 RR

Subgoal 5.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H5.
Subgoal 5.1.2:

Variables: P A Q R1 C1 P2 Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A P2
H6 : at C1 Q1 Q2
============================
 exists RR, one (par R1 Q2) A RR /\ at (par_r P2 C1) Q1 RR

Subgoal 5.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par P2 Q2.
Subgoal 5.1.2:

Variables: P A Q R1 C1 P2 Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 A P2
H6 : at C1 Q1 Q2
============================
 one (par R1 Q2) A (par P2 Q2) /\ at (par_r P2 C1) Q1 (par P2 Q2)

Subgoal 5.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.2:

Variables: P A Q R1 C1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
============================
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply IH to H3 H4.
Subgoal 5.2:

Variables: P A Q R1 C1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H5 : (exists CC, at CC P Q2 /\
          (forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP Q2 /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C1 Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C1 Q Q0 -> one Q0 A Q2)
============================
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H5.
Subgoal 5.2.1:

Variables: P A Q R1 C1 Q2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : at CC P Q2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 5.2.1:

Variables: P A Q R1 C1 Q2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : at CC P Q2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

Subgoal 5.2.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 5.2.1:

Variables: P A Q R1 C1 Q2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : at CC P Q2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 exists CC, at CC P (par R1 Q2) /\
   (forall Q Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC Q RR))

Subgoal 5.2.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_r R1 CC.
Subgoal 5.2.1:

Variables: P A Q R1 C1 Q2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : at CC P Q2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 at (par_r R1 CC) P (par R1 Q2) /\
   (forall Q Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at (par_r R1 CC) Q RR))

Subgoal 5.2.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 5.2.1.1:

Variables: P A Q R1 C1 Q2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : at CC P Q2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 at (par_r R1 CC) P (par R1 Q2)

Subgoal 5.2.1.2 is:
 forall Q Q0, at (par_r R1 C1) Q Q0 ->
   (exists RR, one Q0 A RR /\ at (par_r R1 CC) Q RR)

Subgoal 5.2.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.2.1.2:

Variables: P A Q R1 C1 Q2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : at CC P Q2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
============================
 forall Q Q0, at (par_r R1 C1) Q Q0 ->
   (exists RR, one Q0 A RR /\ at (par_r R1 CC) Q RR)

Subgoal 5.2.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 5.2.1.2:

Variables: P A Q R1 C1 Q2 CC Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : at CC P Q2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H8 : at (par_r R1 C1) Q1 Q0
============================
 exists RR, one Q0 A RR /\ at (par_r R1 CC) Q1 RR

Subgoal 5.2.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H8.
Subgoal 5.2.1.2:

Variables: P A Q R1 C1 Q2 CC Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : at CC P Q2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H9 : at C1 Q1 Q3
============================
 exists RR, one (par R1 Q3) A RR /\ at (par_r R1 CC) Q1 RR

Subgoal 5.2.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H7 to H9.
Subgoal 5.2.1.2:

Variables: P A Q R1 C1 Q2 CC Q1 Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : at CC P Q2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H9 : at C1 Q1 Q3
H10 : one Q3 A RR
H11 : at CC Q1 RR
============================
 exists RR, one (par R1 Q3) A RR /\ at (par_r R1 CC) Q1 RR

Subgoal 5.2.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par R1 RR.
Subgoal 5.2.1.2:

Variables: P A Q R1 C1 Q2 CC Q1 Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : at CC P Q2
H7 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC Q RR)
H9 : at C1 Q1 Q3
H10 : one Q3 A RR
H11 : at CC Q1 RR
============================
 one (par R1 Q3) A (par R1 RR) /\ at (par_r R1 CC) Q1 (par R1 RR)

Subgoal 5.2.2 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.2.2:

Variables: P A Q R1 C1 Q2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 5.2.2:

Variables: P A Q R1 C1 Q2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 5.2.2:

Variables: P A Q R1 C1 Q2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at CC QBQ RR)))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_r R1 CC.
Subgoal 5.2.2:

Variables: P A Q R1 C1 Q2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists PBP B, one P B PBP /\ at (par_r R1 CC) PBP (par R1 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at (par_r R1 CC) QBQ RR)))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness PBP.
Subgoal 5.2.2:

Variables: P A Q R1 C1 Q2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 exists B, one P B PBP /\ at (par_r R1 CC) PBP (par R1 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at (par_r R1 CC) QBQ RR)))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness B.
Subgoal 5.2.2:

Variables: P A Q R1 C1 Q2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 one P B PBP /\ at (par_r R1 CC) PBP (par R1 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 A RR /\ at (par_r R1 CC) QBQ RR)))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 5.2.2.1:

Variables: P A Q R1 C1 Q2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 one P B PBP

Subgoal 5.2.2.2 is:
 at (par_r R1 CC) PBP (par R1 Q2)

Subgoal 5.2.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at (par_r R1 CC) QBQ RR))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.2.2.2:

Variables: P A Q R1 C1 Q2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 at (par_r R1 CC) PBP (par R1 Q2)

Subgoal 5.2.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at (par_r R1 CC) QBQ RR))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.2.2.3:

Variables: P A Q R1 C1 Q2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
============================
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at (par_r R1 CC) QBQ RR))

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 5.2.2.3:

Variables: P A Q R1 C1 Q2 CC PBP B Q1 QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H10 : at (par_r R1 C1) Q1 Q0
============================
 exists RR, one Q0 A RR /\ at (par_r R1 CC) QBQ RR

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H10.
Subgoal 5.2.2.3:

Variables: P A Q R1 C1 Q2 CC PBP B Q1 QBQ Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H11 : at C1 Q1 Q3
============================
 exists RR, one (par R1 Q3) A RR /\ at (par_r R1 CC) QBQ RR

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H8 to H9.
Subgoal 5.2.2.3:

Variables: P A Q R1 C1 Q2 CC PBP B Q1 QBQ Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H11 : at C1 Q1 Q3
H12 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)
============================
 exists RR, one (par R1 Q3) A RR /\ at (par_r R1 CC) QBQ RR

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H12 to H11.
Subgoal 5.2.2.3:

Variables: P A Q R1 C1 Q2 CC PBP B Q1 QBQ Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : one P B PBP
H7 : at CC PBP Q2
H8 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR))
H9 : one Q1 B QBQ
H11 : at C1 Q1 Q3
H12 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 A RR /\ at CC QBQ RR)
H13 : one Q3 A RR
H14 : at CC QBQ RR
============================
 exists RR, one (par R1 Q3) A RR /\ at (par_r R1 CC) QBQ RR

Subgoal 5.2.3 is:
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.2.3:

Variables: P A Q R1 C1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A Q2
============================
 (exists CC, at CC P (par R1 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par R1 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2))

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 5.2.3:

Variables: P A Q R1 C1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A Q2
============================
 forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 A (par R1 Q2)

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 5.2.3:

Variables: P A Q R1 C1 Q2 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A Q2
H7 : at (par_r R1 C1) Q1 Q0
============================
 one Q0 A (par R1 Q2)

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H7.
Subgoal 5.2.3:

Variables: P A Q R1 C1 Q2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A Q2
H8 : at C1 Q1 Q3
============================
 one (par R1 Q3) A (par R1 Q2)

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H6 to H8.
Subgoal 5.2.3:

Variables: P A Q R1 C1 Q2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one Q A Q2
H6 : forall Q Q0, at C1 Q Q0 -> one Q0 A Q2
H8 : at C1 Q1 Q3
H9 : one Q3 A Q2
============================
 one (par R1 Q3) A (par R1 Q2)

Subgoal 5.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.3:

Variables: P Q R1 C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply IH to H3 H5.
Subgoal 5.3:

Variables: P Q R1 C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H6 : (exists CC, at CC P Q2 /\
          (forall Q Q0, at C1 Q Q0 ->
               (exists RR, one Q0 (dn X) RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP Q2 /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C1 Q Q0 ->
                      (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) Q2)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H6.
Subgoal 5.3.1:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 5.3.1:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR))))

Subgoal 5.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 5.3.1:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 exists CC, at CC P (par P2 Q2) /\
   (forall Q Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at CC Q RR))

Subgoal 5.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_r P2 CC.
Subgoal 5.3.1:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 at (par_r P2 CC) P (par P2 Q2) /\
   (forall Q Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_r P2 CC) Q RR))

Subgoal 5.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 5.3.1.1:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 at (par_r P2 CC) P (par P2 Q2)

Subgoal 5.3.1.2 is:
 forall Q Q0, at (par_r R1 C1) Q Q0 ->
   (exists RR, one Q0 tau RR /\ at (par_r P2 CC) Q RR)

Subgoal 5.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.3.1.2:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
============================
 forall Q Q0, at (par_r R1 C1) Q Q0 ->
   (exists RR, one Q0 tau RR /\ at (par_r P2 CC) Q RR)

Subgoal 5.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 5.3.1.2:

Variables: P Q R1 C1 X Q2 P2 CC Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
H9 : at (par_r R1 C1) Q1 Q0
============================
 exists RR, one Q0 tau RR /\ at (par_r P2 CC) Q1 RR

Subgoal 5.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H9.
Subgoal 5.3.1.2:

Variables: P Q R1 C1 X Q2 P2 CC Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
H10 : at C1 Q1 Q3
============================
 exists RR, one (par R1 Q3) tau RR /\ at (par_r P2 CC) Q1 RR

Subgoal 5.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H8 to H10.
Subgoal 5.3.1.2:

Variables: P Q R1 C1 X Q2 P2 CC Q1 Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC Q RR)
H10 : at C1 Q1 Q3
H11 : one Q3 (dn X) RR
H12 : at CC Q1 RR
============================
 exists RR, one (par R1 Q3) tau RR /\ at (par_r P2 CC) Q1 RR

Subgoal 5.3.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.3.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 5.3.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR))))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 5.3.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at CC QBQ RR)))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_r P2 CC.
Subgoal 5.3.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 exists PBP B, one P B PBP /\ at (par_r P2 CC) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR)))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness PBP.
Subgoal 5.3.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 exists B, one P B PBP /\ at (par_r P2 CC) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR)))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness B.
Subgoal 5.3.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 one P B PBP /\ at (par_r P2 CC) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR)))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 5.3.2.1:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 one P B PBP

Subgoal 5.3.2.2 is:
 at (par_r P2 CC) PBP (par P2 Q2)

Subgoal 5.3.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.3.2.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 at (par_r P2 CC) PBP (par P2 Q2)

Subgoal 5.3.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.3.2.3:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
============================
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR))

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 5.3.2.3:

Variables: P Q R1 C1 X Q2 P2 CC PBP B Q1 QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H11 : at (par_r R1 C1) Q1 Q0
============================
 exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H11.
Subgoal 5.3.2.3:

Variables: P Q R1 C1 X Q2 P2 CC PBP B Q1 QBQ Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
============================
 exists RR, one (par R1 Q3) tau RR /\ at (par_r P2 CC) QBQ RR

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H9 to H10.
Subgoal 5.3.2.3:

Variables: P Q R1 C1 X Q2 P2 CC PBP B Q1 QBQ Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
H13 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR)
============================
 exists RR, one (par R1 Q3) tau RR /\ at (par_r P2 CC) QBQ RR

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H13 to H12.
Subgoal 5.3.2.3:

Variables: P Q R1 C1 X Q2 P2 CC PBP B Q1 QBQ Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
H13 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 (dn X) RR /\ at CC QBQ RR)
H14 : one Q3 (dn X) RR
H15 : at CC QBQ RR
============================
 exists RR, one (par R1 Q3) tau RR /\ at (par_r P2 CC) QBQ RR

Subgoal 5.3.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.3.3:

Variables: P Q R1 C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) Q2
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 5.3.3:

Variables: P Q R1 C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) Q2
============================
 forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2)

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 5.3.3:

Variables: P Q R1 C1 X Q2 P2 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) Q2
H8 : at (par_r R1 C1) Q1 Q0
============================
 one Q0 tau (par P2 Q2)

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H8.
Subgoal 5.3.3:

Variables: P Q R1 C1 X Q2 P2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) Q2
H9 : at C1 Q1 Q3
============================
 one (par R1 Q3) tau (par P2 Q2)

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H7 to H9.
Subgoal 5.3.3:

Variables: P Q R1 C1 X Q2 P2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (up X) P2
H5 : one Q (dn X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (dn X) Q2
H9 : at C1 Q1 Q3
H10 : one Q3 (dn X) Q2
============================
 one (par R1 Q3) tau (par P2 Q2)

Subgoal 5.4 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.4:

Variables: P Q R1 C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply IH to H3 H5.
Subgoal 5.4:

Variables: P Q R1 C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H6 : (exists CC, at CC P Q2 /\
          (forall Q Q0, at C1 Q Q0 ->
               (exists RR, one Q0 (up X) RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP Q2 /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C1 Q Q0 ->
                      (exists RR, one Q0 (up X) RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C1 Q Q0 -> one Q0 (up X) Q2)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H6.
Subgoal 5.4.1:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 5.4.1:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR))))

Subgoal 5.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 5.4.1:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 exists CC, at CC P (par P2 Q2) /\
   (forall Q Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at CC Q RR))

Subgoal 5.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_r P2 CC.
Subgoal 5.4.1:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 at (par_r P2 CC) P (par P2 Q2) /\
   (forall Q Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_r P2 CC) Q RR))

Subgoal 5.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 5.4.1.1:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 at (par_r P2 CC) P (par P2 Q2)

Subgoal 5.4.1.2 is:
 forall Q Q0, at (par_r R1 C1) Q Q0 ->
   (exists RR, one Q0 tau RR /\ at (par_r P2 CC) Q RR)

Subgoal 5.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.4.1.2:

Variables: P Q R1 C1 X Q2 P2 CC
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
============================
 forall Q Q0, at (par_r R1 C1) Q Q0 ->
   (exists RR, one Q0 tau RR /\ at (par_r P2 CC) Q RR)

Subgoal 5.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 5.4.1.2:

Variables: P Q R1 C1 X Q2 P2 CC Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
H9 : at (par_r R1 C1) Q1 Q0
============================
 exists RR, one Q0 tau RR /\ at (par_r P2 CC) Q1 RR

Subgoal 5.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H9.
Subgoal 5.4.1.2:

Variables: P Q R1 C1 X Q2 P2 CC Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
H10 : at C1 Q1 Q3
============================
 exists RR, one (par R1 Q3) tau RR /\ at (par_r P2 CC) Q1 RR

Subgoal 5.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H8 to H10.
Subgoal 5.4.1.2:

Variables: P Q R1 C1 X Q2 P2 CC Q1 Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : at CC P Q2
H8 : forall Q Q0, at C1 Q Q0 -> (exists RR, one Q0 (up X) RR /\ at CC Q RR)
H10 : at C1 Q1 Q3
H11 : one Q3 (up X) RR
H12 : at CC Q1 RR
============================
 exists RR, one (par R1 Q3) tau RR /\ at (par_r P2 CC) Q1 RR

Subgoal 5.4.2 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.4.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 5.4.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR))))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 5.4.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at CC QBQ RR)))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness par_r P2 CC.
Subgoal 5.4.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 exists PBP B, one P B PBP /\ at (par_r P2 CC) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR)))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness PBP.
Subgoal 5.4.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 exists B, one P B PBP /\ at (par_r P2 CC) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR)))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < witness B.
Subgoal 5.4.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 one P B PBP /\ at (par_r P2 CC) PBP (par P2 Q2) /\
   (forall Q QBQ, one Q B QBQ ->
        (forall Q0, at (par_r R1 C1) Q Q0 ->
             (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR)))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < split.
Subgoal 5.4.2.1:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 one P B PBP

Subgoal 5.4.2.2 is:
 at (par_r P2 CC) PBP (par P2 Q2)

Subgoal 5.4.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.4.2.2:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 at (par_r P2 CC) PBP (par P2 Q2)

Subgoal 5.4.2.3 is:
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.4.2.3:

Variables: P Q R1 C1 X Q2 P2 CC PBP B
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
============================
 forall Q QBQ, one Q B QBQ ->
   (forall Q0, at (par_r R1 C1) Q Q0 ->
        (exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR))

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 5.4.2.3:

Variables: P Q R1 C1 X Q2 P2 CC PBP B Q1 QBQ Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H11 : at (par_r R1 C1) Q1 Q0
============================
 exists RR, one Q0 tau RR /\ at (par_r P2 CC) QBQ RR

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H11.
Subgoal 5.4.2.3:

Variables: P Q R1 C1 X Q2 P2 CC PBP B Q1 QBQ Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
============================
 exists RR, one (par R1 Q3) tau RR /\ at (par_r P2 CC) QBQ RR

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H9 to H10.
Subgoal 5.4.2.3:

Variables: P Q R1 C1 X Q2 P2 CC PBP B Q1 QBQ Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
H13 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 (up X) RR /\ at CC QBQ RR)
============================
 exists RR, one (par R1 Q3) tau RR /\ at (par_r P2 CC) QBQ RR

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H13 to H12.
Subgoal 5.4.2.3:

Variables: P Q R1 C1 X Q2 P2 CC PBP B Q1 QBQ Q3 RR
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : one P B PBP
H8 : at CC PBP Q2
H9 : forall Q QBQ, one Q B QBQ ->
       (forall Q0, at C1 Q Q0 ->
            (exists RR, one Q0 (up X) RR /\ at CC QBQ RR))
H10 : one Q1 B QBQ
H12 : at C1 Q1 Q3
H13 : forall Q0, at C1 Q1 Q0 -> (exists RR, one Q0 (up X) RR /\ at CC QBQ RR)
H14 : one Q3 (up X) RR
H15 : at CC QBQ RR
============================
 exists RR, one (par R1 Q3) tau RR /\ at (par_r P2 CC) QBQ RR

Subgoal 5.4.3 is:
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 5.4.3:

Variables: P Q R1 C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (up X) Q2
============================
 (exists CC, at CC P (par P2 Q2) /\
      (forall Q Q0, at (par_r R1 C1) Q Q0 ->
           (exists RR, one Q0 tau RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP (par P2 Q2) /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (par_r R1 C1) Q Q0 ->
                  (exists RR, one Q0 tau RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2))

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < right.
Subgoal 5.4.3:

Variables: P Q R1 C1 X Q2 P2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (up X) Q2
============================
 forall Q Q0, at (par_r R1 C1) Q Q0 -> one Q0 tau (par P2 Q2)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < intros.
Subgoal 5.4.3:

Variables: P Q R1 C1 X Q2 P2 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (up X) Q2
H8 : at (par_r R1 C1) Q1 Q0
============================
 one Q0 tau (par P2 Q2)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H8.
Subgoal 5.4.3:

Variables: P Q R1 C1 X Q2 P2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (up X) Q2
H9 : at C1 Q1 Q3
============================
 one (par R1 Q3) tau (par P2 Q2)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < apply H7 to H9.
Subgoal 5.4.3:

Variables: P Q R1 C1 X Q2 P2 Q1 Q3
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (par_r R1 C1) P (par R1 Q) @
H3 : at C1 P Q *
H4 : one R1 (dn X) P2
H5 : one Q (up X) Q2
H7 : forall Q Q0, at C1 Q Q0 -> one Q0 (up X) Q2
H9 : at C1 Q1 Q3
H10 : one Q3 (up X) Q2
============================
 one (par R1 Q3) tau (par P2 Q2)

Subgoal 6 is:
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < search.
Subgoal 6:

Variables: P A R Q A1 C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (act_d A1 C1) P (act A1 Q) @
H2 : one (act A1 Q) A R
H3 : at C1 P Q *
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A1 C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A1 C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A1 C1) Q Q0 -> one Q0 A R)

ctx_faithful < case H2.
Subgoal 6:

Variables: P A R C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (act_d A C1) P (act A R) @
H3 : at C1 P R *
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
   (forall Q Q0, at (act_d A C1) Q Q0 -> one Q0 A R)

ctx_faithful < left.
Subgoal 6:

Variables: P A R C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (act_d A C1) P (act A R) @
H3 : at C1 P R *
============================
 (exists CC, at CC P R /\
      (forall Q Q0, at (act_d A C1) Q Q0 ->
           (exists RR, one Q0 A RR /\ at CC Q RR))) \/
   (exists CC PBP B, one P B PBP /\ at CC PBP R /\
        (forall Q QBQ, one Q B QBQ ->
             (forall Q0, at (act_d A C1) Q Q0 ->
                  (exists RR, one Q0 A RR /\ at CC QBQ RR))))

ctx_faithful < left.
Subgoal 6:

Variables: P A R C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (act_d A C1) P (act A R) @
H3 : at C1 P R *
============================
 exists CC, at CC P R /\
   (forall Q Q0, at (act_d A C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at CC Q RR))

ctx_faithful < witness C1.
Subgoal 6:

Variables: P A R C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (act_d A C1) P (act A R) @
H3 : at C1 P R *
============================
 at C1 P R /\
   (forall Q Q0, at (act_d A C1) Q Q0 ->
        (exists RR, one Q0 A RR /\ at C1 Q RR))

ctx_faithful < split.
Subgoal 6.1:

Variables: P A R C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (act_d A C1) P (act A R) @
H3 : at C1 P R *
============================
 at C1 P R

Subgoal 6.2 is:
 forall Q Q0, at (act_d A C1) Q Q0 -> (exists RR, one Q0 A RR /\ at C1 Q RR)

ctx_faithful < search.
Subgoal 6.2:

Variables: P A R C1
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (act_d A C1) P (act A R) @
H3 : at C1 P R *
============================
 forall Q Q0, at (act_d A C1) Q Q0 -> (exists RR, one Q0 A RR /\ at C1 Q RR)

ctx_faithful < intros.
Subgoal 6.2:

Variables: P A R C1 Q1 Q0
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (act_d A C1) P (act A R) @
H3 : at C1 P R *
H4 : at (act_d A C1) Q1 Q0
============================
 exists RR, one Q0 A RR /\ at C1 Q1 RR

ctx_faithful < case H4.
Subgoal 6.2:

Variables: P A R C1 Q1 Q2
IH : forall C P P0 A R, at C P P0 * -> one P0 A R ->
       (exists CC, at CC P R /\
            (forall Q Q0, at C Q Q0 ->
                 (exists RR, one Q0 A RR /\ at CC Q RR))) \/
       (exists CC PBP B, one P B PBP /\ at CC PBP R /\
            (forall Q QBQ, one Q B QBQ ->
                 (forall Q0, at C Q Q0 ->
                      (exists RR, one Q0 A RR /\ at CC QBQ RR)))) \/
       (forall Q Q0, at C Q Q0 -> one Q0 A R)
H1 : at (act_d A C1) P (act A R) @
H3 : at C1 P R *
H5 : at C1 Q1 Q2
============================
 exists RR, one (act A Q2) A RR /\ at C1 Q1 RR

ctx_faithful < search.
Proof completed.
Abella <