proposition: Lemma gpaco11_weaken clo r rg: gpaco11 (gupaco11 clo) r rg <11= gpaco11 clo r rg.
proof: Proof. intros. apply gpaco11_unfold in PR. induction PR. - destruct IN; cycle 1. apply gpaco11_base, H. apply gpaco11_step_gen. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 H. eapply gpaco11_cofix. intros. apply gpaco11_unfold in PR. induction PR. + destruct IN; cycle 1. apply gpaco11_base, H. apply gpaco11_step. eapply gf_mon. apply H. intros. apply gpaco11_base. apply CIH. eapply gupaco11_mon. apply PR. intros. destruct PR0; apply H0. + apply gpaco11_gupaco. eapply gupaco11_mon. apply IN. apply H. - apply gpaco11_gupaco. eapply gupaco11_mon. apply IN. apply H. Qed.
imports: Program.Basics Paco(paco11 pacotac)