proposition: Lemma gpaco10_weaken clo r rg: gpaco10 (gupaco10 clo) r rg <10= gpaco10 clo r rg.
proof: Proof. intros. apply gpaco10_unfold in PR. induction PR. - destruct IN; cycle 1. apply gpaco10_base, H. apply gpaco10_step_gen. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 H. eapply gpaco10_cofix. intros. apply gpaco10_unfold in PR. induction PR. + destruct IN; cycle 1. apply gpaco10_base, H. apply gpaco10_step. eapply gf_mon. apply H. intros. apply gpaco10_base. apply CIH. eapply gupaco10_mon. apply PR. intros. destruct PR0; apply H0. + apply gpaco10_gupaco. eapply gupaco10_mon. apply IN. apply H. - apply gpaco10_gupaco. eapply gupaco10_mon. apply IN. apply H. Qed.
imports: Program.Basics Paco(paco10 pacotac)