proposition: Lemma Bn_lub : { l | is_lub E l }.
proof: Proof. destruct (completeness E) as [l Hl]. exists 1. unfold is_upper_bound. intros r Hr. destruct Hr as [n Hn]. rewrite <- Hn. apply Bn_maj. exists 0; exists 0%nat. reflexivity. exists l; assumption. Qed.
imports: Reals Lia Lra