proposition: Lemma gpaco9_weaken clo r rg: gpaco9 (gupaco9 clo) r rg <9= gpaco9 clo r rg.
proof: Proof. intros. apply gpaco9_unfold in PR. induction PR. - destruct IN; cycle 1. apply gpaco9_base, H. apply gpaco9_step_gen. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 H. eapply gpaco9_cofix. intros. apply gpaco9_unfold in PR. induction PR. + destruct IN; cycle 1. apply gpaco9_base, H. apply gpaco9_step. eapply gf_mon. apply H. intros. apply gpaco9_base. apply CIH. eapply gupaco9_mon. apply PR. intros. destruct PR0; apply H0. + apply gpaco9_gupaco. eapply gupaco9_mon. apply IN. apply H. - apply gpaco9_gupaco. eapply gupaco9_mon. apply IN. apply H. Qed.
imports: Program.Basics Paco(paco9 pacotac)