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Bug fix: pcofix renamed variable names 'x0,x1' into 'x2,x3'
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@gilhur
gilhur committed Mar 1, 2023
1 parent ec2dd14 commit 5c5693f
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Showing 32 changed files with 96 additions and 96 deletions.
10 changes: 5 additions & 5 deletions metasrc/gpaco.py
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Original file line number Diff line number Diff line change
Expand Up @@ -525,7 +525,7 @@
print (" left. revert"+itrstr(" x", n)+" H.")
print (" pcofix CIH; intros.")
print (" apply rclo"+str(n)+"_wcompat in H0; [|apply gf_mon|apply CMP].")
print (" pstep. eapply gf_mon. apply H0. intros.")
print (" pstep. eapply gf_mon. apply H0. clear "+itrstr(" x", n)+" H0. intros.")
print (" apply gpaco"+str(n)+"_unfold in PR; [|apply gf_mon].")
print (" apply rclo"+str(n)+"_compose in PR.")
print (" apply rclo"+str(n)+"_dist in PR; [|apply CMP|apply DIST].")
Expand All @@ -536,18 +536,18 @@
print (" apply gpaco"+str(n)+"_gupaco. apply gf_mon.")
print (" apply gpaco"+str(n)+"_gen_rclo. apply gf_mon.")
print (" eapply gupaco"+str(n)+"_mon. apply PR0. intros.")
print (" destruct PR1; apply H1.")
print (" destruct PR1; apply H0.")
print (" - assert (REL: @rclo"+str(n)+" clo (rclo"+str(n)+" clo (gf (gupaco"+str(n)+" gf clo ((rg \\"+str(n)+"/ r) \\"+str(n)+"/ (rg \\"+str(n)+"/ r))) \\"+str(n)+"/ (rg \\"+str(n)+"/ r)))"+itrstr(" x", n)+").")
print (" { eapply rclo"+str(n)+"_mon. apply H. intros. apply gpaco"+str(n)+"_unfold in PR. apply PR. apply gf_mon. }")
print (" apply rclo"+str(n)+"_rclo in REL.")
print (" apply rclo"+str(n)+"_dist in REL; [|apply CMP|apply DIST].")
print (" right. destruct REL; cycle 1.")
print (" + apply CIH0, H1.")
print (" + apply CIH0, H0.")
print (" + apply CIH.")
print (" eapply rclo"+str(n)+"_mon. apply H1. intros.")
print (" eapply rclo"+str(n)+"_mon. apply H0. intros.")
print (" eapply gf_mon. apply PR. intros.")
print (" eapply gupaco"+str(n)+"_mon. apply PR0. intros.")
print (" destruct PR1; apply H2.")
print (" destruct PR1; apply H1.")
print ("Qed.")
print ("")
print ("Lemma gpaco"+str(n)+"_dist_reverse clo r rg:")
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2 changes: 1 addition & 1 deletion metasrc/paco.py
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Expand Up @@ -158,7 +158,7 @@
print ("Qed.")
print ("")
print ("Theorem paco"+str(n)+"_acc: forall")
print (" l r (OBG: forall rr (INC: r <"+str(n)+"= rr) (CIH: l <"+str(n)+"= rr), l <"+str(n)+"= paco"+str(n)+" gf rr),")
print (" l r (OBG: forall rr (INC: forall"+itrstr(" _x_",n)+" (PR: r"+itrstr(" _x_",n)+" : Prop), rr"+itrstr(" _x_",n)+" : Prop) (CIH: forall"+itrstr(" _x_",n)+" (PR: l"+itrstr(" _x_",n)+" : Prop), rr"+itrstr(" _x_",n)+" : Prop), forall"+itrstr(" _x_",n)+" (PR: l"+itrstr(" _x_",n)+" : Prop), paco"+str(n)+" gf rr"+itrstr(" _x_",n)+" : Prop),")
print (" l <"+str(n)+"= paco"+str(n)+" gf r.")
print ("Proof.")
print (" apply _paco"+str(n)+"_acc.")
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10 changes: 5 additions & 5 deletions src/gpaco0.v
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Original file line number Diff line number Diff line change
Expand Up @@ -512,7 +512,7 @@ Proof.
left. revert H.
pcofix CIH; intros.
apply rclo0_wcompat in H0; [|apply gf_mon|apply CMP].
pstep. eapply gf_mon. apply H0. intros.
pstep. eapply gf_mon. apply H0. clear H0. intros.
apply gpaco0_unfold in PR; [|apply gf_mon].
apply rclo0_compose in PR.
apply rclo0_dist in PR; [|apply CMP|apply DIST].
Expand All @@ -523,18 +523,18 @@ Proof.
apply gpaco0_gupaco. apply gf_mon.
apply gpaco0_gen_rclo. apply gf_mon.
eapply gupaco0_mon. apply PR0. intros.
destruct PR1; apply H1.
destruct PR1; apply H0.
- assert (REL: @rclo0 clo (rclo0 clo (gf (gupaco0 gf clo ((rg \0/ r) \0/ (rg \0/ r))) \0/ (rg \0/ r)))).
{ eapply rclo0_mon. apply H. intros. apply gpaco0_unfold in PR. apply PR. apply gf_mon. }
apply rclo0_rclo in REL.
apply rclo0_dist in REL; [|apply CMP|apply DIST].
right. destruct REL; cycle 1.
+ apply CIH0, H1.
+ apply CIH0, H0.
+ apply CIH.
eapply rclo0_mon. apply H1. intros.
eapply rclo0_mon. apply H0. intros.
eapply gf_mon. apply PR. intros.
eapply gupaco0_mon. apply PR0. intros.
destruct PR1; apply H2.
destruct PR1; apply H1.
Qed.

Lemma gpaco0_dist_reverse clo r rg:
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10 changes: 5 additions & 5 deletions src/gpaco1.v
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Original file line number Diff line number Diff line change
Expand Up @@ -513,7 +513,7 @@ Proof.
left. revert x0 H.
pcofix CIH; intros.
apply rclo1_wcompat in H0; [|apply gf_mon|apply CMP].
pstep. eapply gf_mon. apply H0. intros.
pstep. eapply gf_mon. apply H0. clear x0 H0. intros.
apply gpaco1_unfold in PR; [|apply gf_mon].
apply rclo1_compose in PR.
apply rclo1_dist in PR; [|apply CMP|apply DIST].
Expand All @@ -524,18 +524,18 @@ Proof.
apply gpaco1_gupaco. apply gf_mon.
apply gpaco1_gen_rclo. apply gf_mon.
eapply gupaco1_mon. apply PR0. intros.
destruct PR1; apply H1.
destruct PR1; apply H0.
- assert (REL: @rclo1 clo (rclo1 clo (gf (gupaco1 gf clo ((rg \1/ r) \1/ (rg \1/ r))) \1/ (rg \1/ r))) x0).
{ eapply rclo1_mon. apply H. intros. apply gpaco1_unfold in PR. apply PR. apply gf_mon. }
apply rclo1_rclo in REL.
apply rclo1_dist in REL; [|apply CMP|apply DIST].
right. destruct REL; cycle 1.
+ apply CIH0, H1.
+ apply CIH0, H0.
+ apply CIH.
eapply rclo1_mon. apply H1. intros.
eapply rclo1_mon. apply H0. intros.
eapply gf_mon. apply PR. intros.
eapply gupaco1_mon. apply PR0. intros.
destruct PR1; apply H2.
destruct PR1; apply H1.
Qed.

Lemma gpaco1_dist_reverse clo r rg:
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10 changes: 5 additions & 5 deletions src/gpaco10.v
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Original file line number Diff line number Diff line change
Expand Up @@ -522,7 +522,7 @@ Proof.
left. revert x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 H.
pcofix CIH; intros.
apply rclo10_wcompat in H0; [|apply gf_mon|apply CMP].
pstep. eapply gf_mon. apply H0. intros.
pstep. eapply gf_mon. apply H0. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 H0. intros.
apply gpaco10_unfold in PR; [|apply gf_mon].
apply rclo10_compose in PR.
apply rclo10_dist in PR; [|apply CMP|apply DIST].
Expand All @@ -533,18 +533,18 @@ Proof.
apply gpaco10_gupaco. apply gf_mon.
apply gpaco10_gen_rclo. apply gf_mon.
eapply gupaco10_mon. apply PR0. intros.
destruct PR1; apply H1.
destruct PR1; apply H0.
- assert (REL: @rclo10 clo (rclo10 clo (gf (gupaco10 gf clo ((rg \10/ r) \10/ (rg \10/ r))) \10/ (rg \10/ r))) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9).
{ eapply rclo10_mon. apply H. intros. apply gpaco10_unfold in PR. apply PR. apply gf_mon. }
apply rclo10_rclo in REL.
apply rclo10_dist in REL; [|apply CMP|apply DIST].
right. destruct REL; cycle 1.
+ apply CIH0, H1.
+ apply CIH0, H0.
+ apply CIH.
eapply rclo10_mon. apply H1. intros.
eapply rclo10_mon. apply H0. intros.
eapply gf_mon. apply PR. intros.
eapply gupaco10_mon. apply PR0. intros.
destruct PR1; apply H2.
destruct PR1; apply H1.
Qed.

Lemma gpaco10_dist_reverse clo r rg:
Expand Down
10 changes: 5 additions & 5 deletions src/gpaco11.v
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Original file line number Diff line number Diff line change
Expand Up @@ -523,7 +523,7 @@ Proof.
left. revert x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 H.
pcofix CIH; intros.
apply rclo11_wcompat in H0; [|apply gf_mon|apply CMP].
pstep. eapply gf_mon. apply H0. intros.
pstep. eapply gf_mon. apply H0. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 H0. intros.
apply gpaco11_unfold in PR; [|apply gf_mon].
apply rclo11_compose in PR.
apply rclo11_dist in PR; [|apply CMP|apply DIST].
Expand All @@ -534,18 +534,18 @@ Proof.
apply gpaco11_gupaco. apply gf_mon.
apply gpaco11_gen_rclo. apply gf_mon.
eapply gupaco11_mon. apply PR0. intros.
destruct PR1; apply H1.
destruct PR1; apply H0.
- assert (REL: @rclo11 clo (rclo11 clo (gf (gupaco11 gf clo ((rg \11/ r) \11/ (rg \11/ r))) \11/ (rg \11/ r))) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10).
{ eapply rclo11_mon. apply H. intros. apply gpaco11_unfold in PR. apply PR. apply gf_mon. }
apply rclo11_rclo in REL.
apply rclo11_dist in REL; [|apply CMP|apply DIST].
right. destruct REL; cycle 1.
+ apply CIH0, H1.
+ apply CIH0, H0.
+ apply CIH.
eapply rclo11_mon. apply H1. intros.
eapply rclo11_mon. apply H0. intros.
eapply gf_mon. apply PR. intros.
eapply gupaco11_mon. apply PR0. intros.
destruct PR1; apply H2.
destruct PR1; apply H1.
Qed.

Lemma gpaco11_dist_reverse clo r rg:
Expand Down
10 changes: 5 additions & 5 deletions src/gpaco12.v
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Expand Up @@ -524,7 +524,7 @@ Proof.
left. revert x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 H.
pcofix CIH; intros.
apply rclo12_wcompat in H0; [|apply gf_mon|apply CMP].
pstep. eapply gf_mon. apply H0. intros.
pstep. eapply gf_mon. apply H0. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 H0. intros.
apply gpaco12_unfold in PR; [|apply gf_mon].
apply rclo12_compose in PR.
apply rclo12_dist in PR; [|apply CMP|apply DIST].
Expand All @@ -535,18 +535,18 @@ Proof.
apply gpaco12_gupaco. apply gf_mon.
apply gpaco12_gen_rclo. apply gf_mon.
eapply gupaco12_mon. apply PR0. intros.
destruct PR1; apply H1.
destruct PR1; apply H0.
- assert (REL: @rclo12 clo (rclo12 clo (gf (gupaco12 gf clo ((rg \12/ r) \12/ (rg \12/ r))) \12/ (rg \12/ r))) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11).
{ eapply rclo12_mon. apply H. intros. apply gpaco12_unfold in PR. apply PR. apply gf_mon. }
apply rclo12_rclo in REL.
apply rclo12_dist in REL; [|apply CMP|apply DIST].
right. destruct REL; cycle 1.
+ apply CIH0, H1.
+ apply CIH0, H0.
+ apply CIH.
eapply rclo12_mon. apply H1. intros.
eapply rclo12_mon. apply H0. intros.
eapply gf_mon. apply PR. intros.
eapply gupaco12_mon. apply PR0. intros.
destruct PR1; apply H2.
destruct PR1; apply H1.
Qed.

Lemma gpaco12_dist_reverse clo r rg:
Expand Down
10 changes: 5 additions & 5 deletions src/gpaco13.v
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Original file line number Diff line number Diff line change
Expand Up @@ -525,7 +525,7 @@ Proof.
left. revert x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 H.
pcofix CIH; intros.
apply rclo13_wcompat in H0; [|apply gf_mon|apply CMP].
pstep. eapply gf_mon. apply H0. intros.
pstep. eapply gf_mon. apply H0. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 H0. intros.
apply gpaco13_unfold in PR; [|apply gf_mon].
apply rclo13_compose in PR.
apply rclo13_dist in PR; [|apply CMP|apply DIST].
Expand All @@ -536,18 +536,18 @@ Proof.
apply gpaco13_gupaco. apply gf_mon.
apply gpaco13_gen_rclo. apply gf_mon.
eapply gupaco13_mon. apply PR0. intros.
destruct PR1; apply H1.
destruct PR1; apply H0.
- assert (REL: @rclo13 clo (rclo13 clo (gf (gupaco13 gf clo ((rg \13/ r) \13/ (rg \13/ r))) \13/ (rg \13/ r))) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12).
{ eapply rclo13_mon. apply H. intros. apply gpaco13_unfold in PR. apply PR. apply gf_mon. }
apply rclo13_rclo in REL.
apply rclo13_dist in REL; [|apply CMP|apply DIST].
right. destruct REL; cycle 1.
+ apply CIH0, H1.
+ apply CIH0, H0.
+ apply CIH.
eapply rclo13_mon. apply H1. intros.
eapply rclo13_mon. apply H0. intros.
eapply gf_mon. apply PR. intros.
eapply gupaco13_mon. apply PR0. intros.
destruct PR1; apply H2.
destruct PR1; apply H1.
Qed.

Lemma gpaco13_dist_reverse clo r rg:
Expand Down
10 changes: 5 additions & 5 deletions src/gpaco14.v
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Original file line number Diff line number Diff line change
Expand Up @@ -526,7 +526,7 @@ Proof.
left. revert x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 H.
pcofix CIH; intros.
apply rclo14_wcompat in H0; [|apply gf_mon|apply CMP].
pstep. eapply gf_mon. apply H0. intros.
pstep. eapply gf_mon. apply H0. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 H0. intros.
apply gpaco14_unfold in PR; [|apply gf_mon].
apply rclo14_compose in PR.
apply rclo14_dist in PR; [|apply CMP|apply DIST].
Expand All @@ -537,18 +537,18 @@ Proof.
apply gpaco14_gupaco. apply gf_mon.
apply gpaco14_gen_rclo. apply gf_mon.
eapply gupaco14_mon. apply PR0. intros.
destruct PR1; apply H1.
destruct PR1; apply H0.
- assert (REL: @rclo14 clo (rclo14 clo (gf (gupaco14 gf clo ((rg \14/ r) \14/ (rg \14/ r))) \14/ (rg \14/ r))) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13).
{ eapply rclo14_mon. apply H. intros. apply gpaco14_unfold in PR. apply PR. apply gf_mon. }
apply rclo14_rclo in REL.
apply rclo14_dist in REL; [|apply CMP|apply DIST].
right. destruct REL; cycle 1.
+ apply CIH0, H1.
+ apply CIH0, H0.
+ apply CIH.
eapply rclo14_mon. apply H1. intros.
eapply rclo14_mon. apply H0. intros.
eapply gf_mon. apply PR. intros.
eapply gupaco14_mon. apply PR0. intros.
destruct PR1; apply H2.
destruct PR1; apply H1.
Qed.

Lemma gpaco14_dist_reverse clo r rg:
Expand Down
10 changes: 5 additions & 5 deletions src/gpaco2.v
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Original file line number Diff line number Diff line change
Expand Up @@ -514,7 +514,7 @@ Proof.
left. revert x0 x1 H.
pcofix CIH; intros.
apply rclo2_wcompat in H0; [|apply gf_mon|apply CMP].
pstep. eapply gf_mon. apply H0. intros.
pstep. eapply gf_mon. apply H0. clear x0 x1 H0. intros.
apply gpaco2_unfold in PR; [|apply gf_mon].
apply rclo2_compose in PR.
apply rclo2_dist in PR; [|apply CMP|apply DIST].
Expand All @@ -525,18 +525,18 @@ Proof.
apply gpaco2_gupaco. apply gf_mon.
apply gpaco2_gen_rclo. apply gf_mon.
eapply gupaco2_mon. apply PR0. intros.
destruct PR1; apply H1.
destruct PR1; apply H0.
- assert (REL: @rclo2 clo (rclo2 clo (gf (gupaco2 gf clo ((rg \2/ r) \2/ (rg \2/ r))) \2/ (rg \2/ r))) x0 x1).
{ eapply rclo2_mon. apply H. intros. apply gpaco2_unfold in PR. apply PR. apply gf_mon. }
apply rclo2_rclo in REL.
apply rclo2_dist in REL; [|apply CMP|apply DIST].
right. destruct REL; cycle 1.
+ apply CIH0, H1.
+ apply CIH0, H0.
+ apply CIH.
eapply rclo2_mon. apply H1. intros.
eapply rclo2_mon. apply H0. intros.
eapply gf_mon. apply PR. intros.
eapply gupaco2_mon. apply PR0. intros.
destruct PR1; apply H2.
destruct PR1; apply H1.
Qed.

Lemma gpaco2_dist_reverse clo r rg:
Expand Down
10 changes: 5 additions & 5 deletions src/gpaco3.v
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Original file line number Diff line number Diff line change
Expand Up @@ -515,7 +515,7 @@ Proof.
left. revert x0 x1 x2 H.
pcofix CIH; intros.
apply rclo3_wcompat in H0; [|apply gf_mon|apply CMP].
pstep. eapply gf_mon. apply H0. intros.
pstep. eapply gf_mon. apply H0. clear x0 x1 x2 H0. intros.
apply gpaco3_unfold in PR; [|apply gf_mon].
apply rclo3_compose in PR.
apply rclo3_dist in PR; [|apply CMP|apply DIST].
Expand All @@ -526,18 +526,18 @@ Proof.
apply gpaco3_gupaco. apply gf_mon.
apply gpaco3_gen_rclo. apply gf_mon.
eapply gupaco3_mon. apply PR0. intros.
destruct PR1; apply H1.
destruct PR1; apply H0.
- assert (REL: @rclo3 clo (rclo3 clo (gf (gupaco3 gf clo ((rg \3/ r) \3/ (rg \3/ r))) \3/ (rg \3/ r))) x0 x1 x2).
{ eapply rclo3_mon. apply H. intros. apply gpaco3_unfold in PR. apply PR. apply gf_mon. }
apply rclo3_rclo in REL.
apply rclo3_dist in REL; [|apply CMP|apply DIST].
right. destruct REL; cycle 1.
+ apply CIH0, H1.
+ apply CIH0, H0.
+ apply CIH.
eapply rclo3_mon. apply H1. intros.
eapply rclo3_mon. apply H0. intros.
eapply gf_mon. apply PR. intros.
eapply gupaco3_mon. apply PR0. intros.
destruct PR1; apply H2.
destruct PR1; apply H1.
Qed.

Lemma gpaco3_dist_reverse clo r rg:
Expand Down
10 changes: 5 additions & 5 deletions src/gpaco4.v
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Original file line number Diff line number Diff line change
Expand Up @@ -516,7 +516,7 @@ Proof.
left. revert x0 x1 x2 x3 H.
pcofix CIH; intros.
apply rclo4_wcompat in H0; [|apply gf_mon|apply CMP].
pstep. eapply gf_mon. apply H0. intros.
pstep. eapply gf_mon. apply H0. clear x0 x1 x2 x3 H0. intros.
apply gpaco4_unfold in PR; [|apply gf_mon].
apply rclo4_compose in PR.
apply rclo4_dist in PR; [|apply CMP|apply DIST].
Expand All @@ -527,18 +527,18 @@ Proof.
apply gpaco4_gupaco. apply gf_mon.
apply gpaco4_gen_rclo. apply gf_mon.
eapply gupaco4_mon. apply PR0. intros.
destruct PR1; apply H1.
destruct PR1; apply H0.
- assert (REL: @rclo4 clo (rclo4 clo (gf (gupaco4 gf clo ((rg \4/ r) \4/ (rg \4/ r))) \4/ (rg \4/ r))) x0 x1 x2 x3).
{ eapply rclo4_mon. apply H. intros. apply gpaco4_unfold in PR. apply PR. apply gf_mon. }
apply rclo4_rclo in REL.
apply rclo4_dist in REL; [|apply CMP|apply DIST].
right. destruct REL; cycle 1.
+ apply CIH0, H1.
+ apply CIH0, H0.
+ apply CIH.
eapply rclo4_mon. apply H1. intros.
eapply rclo4_mon. apply H0. intros.
eapply gf_mon. apply PR. intros.
eapply gupaco4_mon. apply PR0. intros.
destruct PR1; apply H2.
destruct PR1; apply H1.
Qed.

Lemma gpaco4_dist_reverse clo r rg:
Expand Down
10 changes: 5 additions & 5 deletions src/gpaco5.v
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Original file line number Diff line number Diff line change
Expand Up @@ -517,7 +517,7 @@ Proof.
left. revert x0 x1 x2 x3 x4 H.
pcofix CIH; intros.
apply rclo5_wcompat in H0; [|apply gf_mon|apply CMP].
pstep. eapply gf_mon. apply H0. intros.
pstep. eapply gf_mon. apply H0. clear x0 x1 x2 x3 x4 H0. intros.
apply gpaco5_unfold in PR; [|apply gf_mon].
apply rclo5_compose in PR.
apply rclo5_dist in PR; [|apply CMP|apply DIST].
Expand All @@ -528,18 +528,18 @@ Proof.
apply gpaco5_gupaco. apply gf_mon.
apply gpaco5_gen_rclo. apply gf_mon.
eapply gupaco5_mon. apply PR0. intros.
destruct PR1; apply H1.
destruct PR1; apply H0.
- assert (REL: @rclo5 clo (rclo5 clo (gf (gupaco5 gf clo ((rg \5/ r) \5/ (rg \5/ r))) \5/ (rg \5/ r))) x0 x1 x2 x3 x4).
{ eapply rclo5_mon. apply H. intros. apply gpaco5_unfold in PR. apply PR. apply gf_mon. }
apply rclo5_rclo in REL.
apply rclo5_dist in REL; [|apply CMP|apply DIST].
right. destruct REL; cycle 1.
+ apply CIH0, H1.
+ apply CIH0, H0.
+ apply CIH.
eapply rclo5_mon. apply H1. intros.
eapply rclo5_mon. apply H0. intros.
eapply gf_mon. apply PR. intros.
eapply gupaco5_mon. apply PR0. intros.
destruct PR1; apply H2.
destruct PR1; apply H1.
Qed.

Lemma gpaco5_dist_reverse clo r rg:
Expand Down
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