proposition: Lemma grespect4_compatible' clo (RES: grespectful4 clo): compatible'4 (rclo4 (clo \5/ cpn4 gf)).
proof: Proof. apply wrespect4_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn4_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect4_respect) in H; [|apply LE|apply GF]. apply (@compat4_compat gf (rclo4 (cpn4 gf))) in H. 2: { apply rclo4_compat; [apply gf_mon|]. apply cpn4_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo4_clo. right. exists (rclo4 (cpn4 gf)). { apply rclo4_compat; [apply gf_mon|]. apply cpn4_compat. apply gf_mon. } eapply rclo4_mon; [eapply PR|]. intros. eapply rclo4_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn4_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat4_compat gf (rclo4 (cpn4 gf))). { apply rclo4_compat; [apply gf_mon|]. apply cpn4_compat. apply gf_mon. } eapply rclo4_clo_base. eapply cpn4_mon; [apply H|apply GF]. + intros. eapply rclo4_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco4 pacotac)