proposition: Lemma grespect2_compatible' clo (RES: grespectful2 clo): compatible'2 (rclo2 (clo \3/ cpn2 gf)).
proof: Proof. apply wrespect2_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn2_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect2_respect) in H; [|apply LE|apply GF]. apply (@compat2_compat gf (rclo2 (cpn2 gf))) in H. 2: { apply rclo2_compat; [apply gf_mon|]. apply cpn2_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo2_clo. right. exists (rclo2 (cpn2 gf)). { apply rclo2_compat; [apply gf_mon|]. apply cpn2_compat. apply gf_mon. } eapply rclo2_mon; [eapply PR|]. intros. eapply rclo2_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn2_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat2_compat gf (rclo2 (cpn2 gf))). { apply rclo2_compat; [apply gf_mon|]. apply cpn2_compat. apply gf_mon. } eapply rclo2_clo_base. eapply cpn2_mon; [apply H|apply GF]. + intros. eapply rclo2_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco2 pacotac)