proposition: Lemma grespect0_compatible' clo (RES: grespectful0 clo): compatible'0 (rclo0 (clo \1/ cpn0 gf)).
proof: Proof. apply wrespect0_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn0_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect0_respect) in H; [|apply LE|apply GF]. apply (@compat0_compat gf (rclo0 (cpn0 gf))) in H. 2: { apply rclo0_compat; [apply gf_mon|]. apply cpn0_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo0_clo. right. exists (rclo0 (cpn0 gf)). { apply rclo0_compat; [apply gf_mon|]. apply cpn0_compat. apply gf_mon. } eapply rclo0_mon; [eapply PR|]. intros. eapply rclo0_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn0_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat0_compat gf (rclo0 (cpn0 gf))). { apply rclo0_compat; [apply gf_mon|]. apply cpn0_compat. apply gf_mon. } eapply rclo0_clo_base. eapply cpn0_mon; [apply H|apply GF]. + intros. eapply rclo0_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco0 pacotac)