proposition: Lemma gpaco7_weaken clo r rg: gpaco7 (gupaco7 clo) r rg <7= gpaco7 clo r rg.
proof: Proof. intros. apply gpaco7_unfold in PR. induction PR. - destruct IN; cycle 1. apply gpaco7_base, H. apply gpaco7_step_gen. eapply gf_mon. apply H. clear x0 x1 x2 x3 x4 x5 x6 H. eapply gpaco7_cofix. intros. apply gpaco7_unfold in PR. induction PR. + destruct IN; cycle 1. apply gpaco7_base, H. apply gpaco7_step. eapply gf_mon. apply H. intros. apply gpaco7_base. apply CIH. eapply gupaco7_mon. apply PR. intros. destruct PR0; apply H0. + apply gpaco7_gupaco. eapply gupaco7_mon. apply IN. apply H. - apply gpaco7_gupaco. eapply gupaco7_mon. apply IN. apply H. Qed.
imports: Program.Basics Paco(paco7 pacotac)