proposition: Lemma grespect3_compatible' clo (RES: grespectful3 clo): compatible'3 (rclo3 (clo \4/ cpn3 gf)).
proof: Proof. apply wrespect3_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn3_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect3_respect) in H; [|apply LE|apply GF]. apply (@compat3_compat gf (rclo3 (cpn3 gf))) in H. 2: { apply rclo3_compat; [apply gf_mon|]. apply cpn3_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo3_clo. right. exists (rclo3 (cpn3 gf)). { apply rclo3_compat; [apply gf_mon|]. apply cpn3_compat. apply gf_mon. } eapply rclo3_mon; [eapply PR|]. intros. eapply rclo3_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn3_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat3_compat gf (rclo3 (cpn3 gf))). { apply rclo3_compat; [apply gf_mon|]. apply cpn3_compat. apply gf_mon. } eapply rclo3_clo_base. eapply cpn3_mon; [apply H|apply GF]. + intros. eapply rclo3_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco3 pacotac)