proposition: Lemma grespect8_compatible' clo (RES: grespectful8 clo): compatible'8 (rclo8 (clo \9/ cpn8 gf)).
proof: Proof. apply wrespect8_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn8_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect8_respect) in H; [|apply LE|apply GF]. apply (@compat8_compat gf (rclo8 (cpn8 gf))) in H. 2: { apply rclo8_compat; [apply gf_mon|]. apply cpn8_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo8_clo. right. exists (rclo8 (cpn8 gf)). { apply rclo8_compat; [apply gf_mon|]. apply cpn8_compat. apply gf_mon. } eapply rclo8_mon; [eapply PR|]. intros. eapply rclo8_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn8_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat8_compat gf (rclo8 (cpn8 gf))). { apply rclo8_compat; [apply gf_mon|]. apply cpn8_compat. apply gf_mon. } eapply rclo8_clo_base. eapply cpn8_mon; [apply H|apply GF]. + intros. eapply rclo8_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco8 pacotac)