proposition: Lemma gpaco13_gpaco clo r rg: gpaco13 clo (gpaco13 clo r rg) (gupaco13 clo (rg \13/ r)) <13= gpaco13 clo r rg.
proof: Proof. intros. apply gpaco13_unfold in PR. econstructor. apply rclo13_rclo. eapply rclo13_mon. apply PR. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 PR. intros. destruct PR; [|destruct H; apply IN]. apply rclo13_base. left. pstep. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 H. intros. cut (@gupaco13 clo (rg \13/ r) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12). { intros. destruct H. eapply rclo13_mon. apply IN. intros. destruct PR0; [|right; apply H]. left. eapply paco13_mon. apply H. intros. destruct PR0; apply H0. } apply gpaco13_gupaco. eapply gupaco13_mon. apply PR. intros. destruct PR0; [apply H|]. eapply gpaco13_mon; [apply H|right|left]; intros; apply PR0. Qed.
imports: Program.Basics Paco(paco13 pacotac)