proposition: Lemma gpaco3_gpaco clo r rg: gpaco3 clo (gpaco3 clo r rg) (gupaco3 clo (rg \3/ r)) <3= gpaco3 clo r rg.
proof: Proof. intros. apply gpaco3_unfold in PR. econstructor. apply rclo3_rclo. eapply rclo3_mon. apply PR. clear x0 x1 x2 PR. intros. destruct PR; [|destruct H; apply IN]. apply rclo3_base. left. pstep. eapply gf_mon. apply H. clear x0 x1 x2 H. intros. cut (@gupaco3 clo (rg \3/ r) x0 x1 x2). { intros. destruct H. eapply rclo3_mon. apply IN. intros. destruct PR0; [|right; apply H]. left. eapply paco3_mon. apply H. intros. destruct PR0; apply H0. } apply gpaco3_gupaco. eapply gupaco3_mon. apply PR. intros. destruct PR0; [apply H|]. eapply gpaco3_mon; [apply H|right|left]; intros; apply PR0. Qed.
imports: Program.Basics Paco(paco3 pacotac)