proposition: Lemma grespect12_compatible' clo (RES: grespectful12 clo): compatible'12 (rclo12 (clo \13/ cpn12 gf)).
proof: Proof. apply wrespect12_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn12_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect12_respect) in H; [|apply LE|apply GF]. apply (@compat12_compat gf (rclo12 (cpn12 gf))) in H. 2: { apply rclo12_compat; [apply gf_mon|]. apply cpn12_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo12_clo. right. exists (rclo12 (cpn12 gf)). { apply rclo12_compat; [apply gf_mon|]. apply cpn12_compat. apply gf_mon. } eapply rclo12_mon; [eapply PR|]. intros. eapply rclo12_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn12_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat12_compat gf (rclo12 (cpn12 gf))). { apply rclo12_compat; [apply gf_mon|]. apply cpn12_compat. apply gf_mon. } eapply rclo12_clo_base. eapply cpn12_mon; [apply H|apply GF]. + intros. eapply rclo12_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco12 pacotac)