proposition: Lemma grespect1_compatible' clo (RES: grespectful1 clo): compatible'1 (rclo1 (clo \2/ cpn1 gf)).
proof: Proof. apply wrespect1_compatible'. econstructor. { red; intros. destruct IN. - left. eapply RES; [apply H|]. apply LE. - right. eapply cpn1_mon; [apply H|]. apply LE. } intros. destruct PR. - eapply RES.(grespect1_respect) in H; [|apply LE|apply GF]. apply (@compat1_compat gf (rclo1 (cpn1 gf))) in H. 2: { apply rclo1_compat; [apply gf_mon|]. apply cpn1_compat. apply gf_mon. } eapply gf_mon; [apply H|]. intros. apply rclo1_clo. right. exists (rclo1 (cpn1 gf)). { apply rclo1_compat; [apply gf_mon|]. apply cpn1_compat. apply gf_mon. } eapply rclo1_mon; [eapply PR|]. intros. eapply rclo1_mon_gen; [eapply PR0|..]. + intros. destruct PR1. * left. apply H0. * right. apply cpn1_gupaco; [apply gf_mon|apply H0]. + intros. apply PR1. - eapply gf_mon. + apply (@compat1_compat gf (rclo1 (cpn1 gf))). { apply rclo1_compat; [apply gf_mon|]. apply cpn1_compat. apply gf_mon. } eapply rclo1_clo_base. eapply cpn1_mon; [apply H|apply GF]. + intros. eapply rclo1_mon_gen; [eapply PR|..]. * intros. right. apply PR0. * intros. apply PR0. Qed.
imports: Program.Basics Paco(paco1 pacotac)