proposition: Lemma grespect10_compatible' clo (RES: grespectful10 clo): compatible'10 (rclo10 (clo \11/ cpn10 gf)).
proof: Proof. apply wrespect10_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn10_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect10_respect) in H; [|apply LE|apply GF]. apply (@compat10_compat gf (rclo10 (cpn10 gf))) in H. 2: { apply rclo10_compat; [apply gf_mon|]. apply cpn10_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo10_clo. right. exists (rclo10 (cpn10 gf)). { apply rclo10_compat; [apply gf_mon|]. apply cpn10_compat. apply gf_mon. } eapply rclo10_mon; [eapply PR|]. intros. eapply rclo10_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn10_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat10_compat gf (rclo10 (cpn10 gf))). { apply rclo10_compat; [apply gf_mon|]. apply cpn10_compat. apply gf_mon. } eapply rclo10_clo_base. eapply cpn10_mon; [apply H|apply GF]. + intros. eapply rclo10_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco10 pacotac)