proposition: Lemma gpaco11_gpaco clo r rg: gpaco11 clo (gpaco11 clo r rg) (gupaco11 clo (rg \11/ r)) <11= gpaco11 clo r rg.
proof: Proof. intros. apply gpaco11_unfold in PR. econstructor. apply rclo11_rclo. eapply rclo11_mon. apply PR. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 PR. intros. destruct PR; [|destruct H; apply IN]. apply rclo11_base. left. pstep. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 H. intros. cut (@gupaco11 clo (rg \11/ r) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10). { intros. destruct H. eapply rclo11_mon. apply IN. intros. destruct PR0; [|right; apply H]. left. eapply paco11_mon. apply H. intros. destruct PR0; apply H0. } apply gpaco11_gupaco. eapply gupaco11_mon. apply PR. intros. destruct PR0; [apply H|]. eapply gpaco11_mon; [apply H|right|left]; intros; apply PR0. Qed.
imports: Program.Basics Paco(paco11 pacotac)