proposition: Lemma wrespect12_compatible' clo (RES: wrespectful12 clo): compatible'12 (rclo12 clo).
proof: Proof. intros. econstructor. apply rclo12_mon. intros. destruct RES. split. { eapply rclo12_mon. apply PR. intros. apply PR0. } induction PR; intros. - eapply gf_mon. apply IN. intros. apply rclo12_base, PR. - eapply gf_mon. + eapply wrespect12_respect0; [|apply H|apply IN]. intros. eapply rclo12_mon; intros; [apply LE, PR|apply PR0]. + intros. apply rclo12_rclo, PR. Qed.
imports: Program.Basics Paco(paco12 pacotac)