proposition: Lemma gpaco4_gpaco clo r rg: gpaco4 clo (gpaco4 clo r rg) (gupaco4 clo (rg \4/ r)) <4= gpaco4 clo r rg.
proof: Proof. intros. apply gpaco4_unfold in PR. econstructor. apply rclo4_rclo. eapply rclo4_mon. apply PR. clear x0 x1 x2 x3 PR. intros. destruct PR; [|destruct H; apply IN]. apply rclo4_base. left. pstep. eapply gf_mon. apply H. clear x0 x1 x2 x3 H. intros. cut (@gupaco4 clo (rg \4/ r) x0 x1 x2 x3). { intros. destruct H. eapply rclo4_mon. apply IN. intros. destruct PR0; [|right; apply H]. left. eapply paco4_mon. apply H. intros. destruct PR0; apply H0. } apply gpaco4_gupaco. eapply gupaco4_mon. apply PR. intros. destruct PR0; [apply H|]. eapply gpaco4_mon; [apply H|right|left]; intros; apply PR0. Qed.
imports: Program.Basics Paco(paco4 pacotac)