proposition: Lemma gpaco5_weaken clo r rg: gpaco5 (gupaco5 clo) r rg <5= gpaco5 clo r rg.
proof: Proof. intros. apply gpaco5_unfold in PR. induction PR. - destruct IN; cycle 1. apply gpaco5_base, H. apply gpaco5_step_gen. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 H. eapply gpaco5_cofix. intros. apply gpaco5_unfold in PR. induction PR. + destruct IN; cycle 1. apply gpaco5_base, H. apply gpaco5_step. eapply gf_mon. apply H. intros. apply gpaco5_base. apply CIH. eapply gupaco5_mon. apply PR. intros. destruct PR0; apply H0. + apply gpaco5_gupaco. eapply gupaco5_mon. apply IN. apply H. - apply gpaco5_gupaco. eapply gupaco5_mon. apply IN. apply H. Qed.
imports: Program.Basics Paco(paco5 pacotac)