proposition: Lemma grespect14_compatible' clo (RES: grespectful14 clo): compatible'14 (rclo14 (clo \15/ cpn14 gf)).
proof: Proof. apply wrespect14_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn14_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect14_respect) in H; [|apply LE|apply GF]. apply (@compat14_compat gf (rclo14 (cpn14 gf))) in H. 2: { apply rclo14_compat; [apply gf_mon|]. apply cpn14_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo14_clo. right. exists (rclo14 (cpn14 gf)). { apply rclo14_compat; [apply gf_mon|]. apply cpn14_compat. apply gf_mon. } eapply rclo14_mon; [eapply PR|]. intros. eapply rclo14_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn14_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat14_compat gf (rclo14 (cpn14 gf))). { apply rclo14_compat; [apply gf_mon|]. apply cpn14_compat. apply gf_mon. } eapply rclo14_clo_base. eapply cpn14_mon; [apply H|apply GF]. + intros. eapply rclo14_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco14 pacotac)