proposition: Lemma grespect5_compatible' clo (RES: grespectful5 clo): compatible'5 (rclo5 (clo \6/ cpn5 gf)).
proof: Proof. apply wrespect5_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn5_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect5_respect) in H; [|apply LE|apply GF]. apply (@compat5_compat gf (rclo5 (cpn5 gf))) in H. 2: { apply rclo5_compat; [apply gf_mon|]. apply cpn5_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo5_clo. right. exists (rclo5 (cpn5 gf)). { apply rclo5_compat; [apply gf_mon|]. apply cpn5_compat. apply gf_mon. } eapply rclo5_mon; [eapply PR|]. intros. eapply rclo5_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn5_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat5_compat gf (rclo5 (cpn5 gf))). { apply rclo5_compat; [apply gf_mon|]. apply cpn5_compat. apply gf_mon. } eapply rclo5_clo_base. eapply cpn5_mon; [apply H|apply GF]. + intros. eapply rclo5_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco5 pacotac)