proposition: Lemma gpaco10_gpaco clo r rg: gpaco10 clo (gpaco10 clo r rg) (gupaco10 clo (rg \10/ r)) <10= gpaco10 clo r rg.
proof: Proof. intros. apply gpaco10_unfold in PR. econstructor. apply rclo10_rclo. eapply rclo10_mon. apply PR. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 PR. intros. destruct PR; [|destruct H; apply IN]. apply rclo10_base. left. pstep. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 H. intros. cut (@gupaco10 clo (rg \10/ r) x0 x1 x2 x3 x4 x5 x6 x7 x8 x9). { intros. destruct H. eapply rclo10_mon. apply IN. intros. destruct PR0; [|right; apply H]. left. eapply paco10_mon. apply H. intros. destruct PR0; apply H0. } apply gpaco10_gupaco. eapply gupaco10_mon. apply PR. intros. destruct PR0; [apply H|]. eapply gpaco10_mon; [apply H|right|left]; intros; apply PR0. Qed.
imports: Program.Basics Paco(paco10 pacotac)