proposition: Lemma gpaco6_dist clo r rg (CMP: wcompatible6 gf clo) (DIST: forall r1 r2, clo (r1 \6/ r2) <6= (clo r1 \6/ clo r2)): gpaco6 gf clo r rg <6= (paco6 gf (rclo6 clo (rg \6/ r)) \6/ rclo6 clo r).
proof: Proof. intros. apply gpaco6_unfold in PR; [|apply gf_mon]. apply rclo6_dist in PR; [|apply CMP|apply DIST]. destruct PR; [|right; apply H]. left. revert x0 x1 x2 x3 x4 x5 H. pcofix CIH; intros. apply rclo6_wcompat in H0; [|apply gf_mon|apply CMP]. pstep. eapply gf_mon. apply H0. clear x0 x1 x2 x3 x4 x5 H0. intros. apply gpaco6_unfold in PR; [|apply gf_mon]. apply rclo6_compose in PR. apply rclo6_dist in PR; [|apply CMP|apply DIST]. destruct PR. - right. apply CIH. eapply rclo6_mon. apply H. intros. eapply gf_mon. apply PR. intros. apply gpaco6_gupaco. apply gf_mon. apply gpaco6_gen_rclo. apply gf_mon. eapply gupaco6_mon. apply PR0. intros. destruct PR1; apply H0. - assert (REL: @rclo6 clo (rclo6 clo (gf (gupaco6 gf clo ((rg \6/ r) \6/ (rg \6/ r))) \6/ (rg \6/ r))) x0 x1 x2 x3 x4 x5). { eapply rclo6_mon. apply H. intros. apply gpaco6_unfold in PR. apply PR. apply gf_mon. } apply rclo6_rclo in REL. apply rclo6_dist in REL; [|apply CMP|apply DIST]. right. destruct REL; cycle 1. + apply CIH0, H0. + apply CIH. eapply rclo6_mon. apply H0. intros. eapply gf_mon. apply PR. intros. eapply gupaco6_mon. apply PR0. intros. destruct PR1; apply H1. Qed.
imports: Program.Basics Paco(paco6 pacotac)