proposition: Lemma Cbigger : forall x y : R, {z : R | x [<=] z | y [<=] z}.
proof: Proof. intros. elim (less_cotransitive_unfolded _ x (x[+][1]) (less_plusOne _ _) y); intro. exists (y[+][1]); apply less_leEq. apply less_leEq_trans with y. auto. apply less_leEq; apply less_plusOne. apply less_plusOne. exists (x[+][1]); apply less_leEq. apply less_plusOne. auto. Qed.
imports: CoRN.reals.IVT