proposition: Lemma gpaco8_weaken clo r rg: gpaco8 (gupaco8 clo) r rg <8= gpaco8 clo r rg.
proof: Proof. intros. apply gpaco8_unfold in PR. induction PR. - destruct IN; cycle 1. apply gpaco8_base, H. apply gpaco8_step_gen. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 x7 H. eapply gpaco8_cofix. intros. apply gpaco8_unfold in PR. induction PR. + destruct IN; cycle 1. apply gpaco8_base, H. apply gpaco8_step. eapply gf_mon. apply H. intros. apply gpaco8_base. apply CIH. eapply gupaco8_mon. apply PR. intros. destruct PR0; apply H0. + apply gpaco8_gupaco. eapply gupaco8_mon. apply IN. apply H. - apply gpaco8_gupaco. eapply gupaco8_mon. apply IN. apply H. Qed.
imports: Program.Basics Paco(paco8 pacotac)