proposition: Lemma IVT'_I : {x : IR | I' x | forall Hx, F x Hx [=] z}.
proof: Proof. elim (IVT_I a b Hab' Hab F contF) with z; try apply less_leEq; auto. intros x H H0. exists x; auto. elim H; intros; split; apply leEq_not_eq; auto. apply pfstrx with F (incF _ Ha) (incF _ H). apply less_imp_ap; astepr z; auto. apply pfstrx with F (incF _ H) (incF _ Hb). apply less_imp_ap; astepl z; auto. Qed.
imports: CoRN.ftc.WeakIVT CoRN.ftc.CalculusTheorems