proposition: Lemma gpaco14_gpaco clo r rg: gpaco14 clo (gpaco14 clo r rg) (gupaco14 clo (rg \14/ r)) <14= gpaco14 clo r rg.
proof: Proof. intros. apply gpaco14_unfold in PR. econstructor. apply rclo14_rclo. eapply rclo14_mon. apply PR. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 PR. intros. destruct PR; [|destruct H; apply IN]. apply rclo14_base. left. pstep. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 H. intros. cut (@gupaco14 clo (rg \14/ r) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13). { intros. destruct H. eapply rclo14_mon. apply IN. intros. destruct PR0; [|right; apply H]. left. eapply paco14_mon. apply H. intros. destruct PR0; apply H0. } apply gpaco14_gupaco. eapply gupaco14_mon. apply PR. intros. destruct PR0; [apply H|]. eapply gpaco14_mon; [apply H|right|left]; intros; apply PR0. Qed.
imports: Program.Basics Paco(paco14 pacotac)