proposition: Lemma grespect6_compatible' clo (RES: grespectful6 clo): compatible'6 (rclo6 (clo \7/ cpn6 gf)).
proof: Proof. apply wrespect6_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn6_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect6_respect) in H; [|apply LE|apply GF]. apply (@compat6_compat gf (rclo6 (cpn6 gf))) in H. 2: { apply rclo6_compat; [apply gf_mon|]. apply cpn6_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo6_clo. right. exists (rclo6 (cpn6 gf)). { apply rclo6_compat; [apply gf_mon|]. apply cpn6_compat. apply gf_mon. } eapply rclo6_mon; [eapply PR|]. intros. eapply rclo6_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn6_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat6_compat gf (rclo6 (cpn6 gf))). { apply rclo6_compat; [apply gf_mon|]. apply cpn6_compat. apply gf_mon. } eapply rclo6_clo_base. eapply cpn6_mon; [apply H|apply GF]. + intros. eapply rclo6_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco6 pacotac)