proposition: Lemma gpaco8_gpaco clo r rg: gpaco8 clo (gpaco8 clo r rg) (gupaco8 clo (rg \8/ r)) <8= gpaco8 clo r rg.
proof: Proof. intros. apply gpaco8_unfold in PR. econstructor. apply rclo8_rclo. eapply rclo8_mon. apply PR. clear x0 x1 x2 x3 x4 x5 x6 x7 PR. intros. destruct PR; [|destruct H; apply IN]. apply rclo8_base. left. pstep. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 x7 H. intros. cut (@gupaco8 clo (rg \8/ r) x0 x1 x2 x3 x4 x5 x6 x7). { intros. destruct H. eapply rclo8_mon. apply IN. intros. destruct PR0; [|right; apply H]. left. eapply paco8_mon. apply H. intros. destruct PR0; apply H0. } apply gpaco8_gupaco. eapply gupaco8_mon. apply PR. intros. destruct PR0; [apply H|]. eapply gpaco8_mon; [apply H|right|left]; intros; apply PR0. Qed.
imports: Program.Basics Paco(paco8 pacotac)