proposition: Lemma grespect9_compatible' clo (RES: grespectful9 clo): compatible'9 (rclo9 (clo \10/ cpn9 gf)).
proof: Proof. apply wrespect9_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn9_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect9_respect) in H; [|apply LE|apply GF]. apply (@compat9_compat gf (rclo9 (cpn9 gf))) in H. 2: { apply rclo9_compat; [apply gf_mon|]. apply cpn9_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo9_clo. right. exists (rclo9 (cpn9 gf)). { apply rclo9_compat; [apply gf_mon|]. apply cpn9_compat. apply gf_mon. } eapply rclo9_mon; [eapply PR|]. intros. eapply rclo9_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn9_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat9_compat gf (rclo9 (cpn9 gf))). { apply rclo9_compat; [apply gf_mon|]. apply cpn9_compat. apply gf_mon. } eapply rclo9_clo_base. eapply cpn9_mon; [apply H|apply GF]. + intros. eapply rclo9_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco9 pacotac)