proposition: Lemma mu_mufix_le : forall x, mu (Mfix F x) (q x) <= mufix muF x.
proof: Proof. intros; unfold mufix,Mfix,mu_lub; simpl. apply lub_le_compat; intros. intro n; generalize x; induction n; simpl; intros; auto. apply Ole_trans with (muF (fun y => mu (Miter F n y) (q y)) x0). apply F_muF_le. unfold Mfix,fixp; intros. apply le_lub. apply (fmonotonic muF); auto. Qed.
imports: ALEA(Probas) ALEA(Utheory)