proposition: Lemma grespect13_compatible' clo (RES: grespectful13 clo): compatible'13 (rclo13 (clo \14/ cpn13 gf)).
proof: Proof. apply wrespect13_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn13_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect13_respect) in H; [|apply LE|apply GF]. apply (@compat13_compat gf (rclo13 (cpn13 gf))) in H. 2: { apply rclo13_compat; [apply gf_mon|]. apply cpn13_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo13_clo. right. exists (rclo13 (cpn13 gf)). { apply rclo13_compat; [apply gf_mon|]. apply cpn13_compat. apply gf_mon. } eapply rclo13_mon; [eapply PR|]. intros. eapply rclo13_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn13_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat13_compat gf (rclo13 (cpn13 gf))). { apply rclo13_compat; [apply gf_mon|]. apply cpn13_compat. apply gf_mon. } eapply rclo13_clo_base. eapply cpn13_mon; [apply H|apply GF]. + intros. eapply rclo13_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco13 pacotac)