proposition: Lemma gpaco2_gpaco clo r rg: gpaco2 clo (gpaco2 clo r rg) (gupaco2 clo (rg \2/ r)) <2= gpaco2 clo r rg.
proof: Proof. intros. apply gpaco2_unfold in PR. econstructor. apply rclo2_rclo. eapply rclo2_mon. apply PR. clear x0 x1 PR. intros. destruct PR; [|destruct H; apply IN]. apply rclo2_base. left. pstep. eapply gf_mon. apply H. clear x0 x1 H. intros. cut (@gupaco2 clo (rg \2/ r) x0 x1). { intros. destruct H. eapply rclo2_mon. apply IN. intros. destruct PR0; [|right; apply H]. left. eapply paco2_mon. apply H. intros. destruct PR0; apply H0. } apply gpaco2_gupaco. eapply gupaco2_mon. apply PR. intros. destruct PR0; [apply H|]. eapply gpaco2_mon; [apply H|right|left]; intros; apply PR0. Qed.
imports: Program.Basics Paco(paco2 pacotac)