proposition: Lemma gpaco9_gpaco clo r rg: gpaco9 clo (gpaco9 clo r rg) (gupaco9 clo (rg \9/ r)) <9= gpaco9 clo r rg.
proof: Proof. intros. apply gpaco9_unfold in PR. econstructor. apply rclo9_rclo. eapply rclo9_mon. apply PR. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 PR. intros. destruct PR; [|destruct H; apply IN]. apply rclo9_base. left. pstep. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 H. intros. cut (@gupaco9 clo (rg \9/ r) x0 x1 x2 x3 x4 x5 x6 x7 x8). { intros. destruct H. eapply rclo9_mon. apply IN. intros. destruct PR0; [|right; apply H]. left. eapply paco9_mon. apply H. intros. destruct PR0; apply H0. } apply gpaco9_gupaco. eapply gupaco9_mon. apply PR. intros. destruct PR0; [apply H|]. eapply gpaco9_mon; [apply H|right|left]; intros; apply PR0. Qed.
imports: Program.Basics Paco(paco9 pacotac)