proposition: Lemma gpaco5_gpaco clo r rg: gpaco5 clo (gpaco5 clo r rg) (gupaco5 clo (rg \5/ r)) <5= gpaco5 clo r rg.
proof: Proof. intros. apply gpaco5_unfold in PR. econstructor. apply rclo5_rclo. eapply rclo5_mon. apply PR. clear x0 x1 x2 x3 x4 PR. intros. destruct PR; [|destruct H; apply IN]. apply rclo5_base. left. pstep. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 H. intros. cut (@gupaco5 clo (rg \5/ r) x0 x1 x2 x3 x4). { intros. destruct H. eapply rclo5_mon. apply IN. intros. destruct PR0; [|right; apply H]. left. eapply paco5_mon. apply H. intros. destruct PR0; apply H0. } apply gpaco5_gupaco. eapply gupaco5_mon. apply PR. intros. destruct PR0; [apply H|]. eapply gpaco5_mon; [apply H|right|left]; intros; apply PR0. Qed.
imports: Program.Basics Paco(paco5 pacotac)