proposition: Lemma cont_no_sign_change_pos : forall e, [0] [<] e -> forall x y, I x -> I y -> forall Hx Hy, AbsIR (F x Hx[-]F y Hy) [<=] e -> e [<] AbsIR (F x Hx) -> e [<] F x Hx -> [0] [<] F y Hy.
proof: Proof. intros e H x y H0 H1 Hx Hy H2 H3 H4. elim (cont_no_sign_change e H x y H0 H1 Hx Hy H2 H3); intros H5 H6. apply H5. apply less_transitive_unfolded with e; auto. Qed.
imports: CoRN.reals.NRootIR CoRN.ftc.FunctSums CoRN.tactics.CornTac