proposition: Lemma muF_le_term : forall f, muFqinv (finv f) <= finv f -> forall x, f x & pterm x <= mu (Mfix F x) (q x).
proof: Proof. intros; apply Ole_trans with (mu (Mfix F x) (fesp (q x) (fone B))). apply Ole_trans with ([1-] mu (Mfix F x) (qinv x) & pterm x). apply Uesp_le_compat; auto. apply Uinv_le_perm_right. apply muF_le with (muF:=muFqinv) (q:=qinv) (f:=finv f) (x:=x); auto. unfold pterm; replace (qinv x) with (finv (q x)); auto. apply mu_monotonic; intro; unfold fesp,fone; repeat Usimpl; auto. Qed.
imports: ALEA(Probas) ALEA(Utheory)