proposition: Lemma gpaco12_weaken clo r rg: gpaco12 (gupaco12 clo) r rg <12= gpaco12 clo r rg.
proof: Proof. intros. apply gpaco12_unfold in PR. induction PR. - destruct IN; cycle 1. apply gpaco12_base, H. apply gpaco12_step_gen. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 H. eapply gpaco12_cofix. intros. apply gpaco12_unfold in PR. induction PR. + destruct IN; cycle 1. apply gpaco12_base, H. apply gpaco12_step. eapply gf_mon. apply H. intros. apply gpaco12_base. apply CIH. eapply gupaco12_mon. apply PR. intros. destruct PR0; apply H0. + apply gpaco12_gupaco. eapply gupaco12_mon. apply IN. apply H. - apply gpaco12_gupaco. eapply gupaco12_mon. apply IN. apply H. Qed.
imports: Program.Basics Paco(paco12 pacotac)