proposition: Lemma EOlt_le : ∏ x y : X, x < y -> x <= y.
proof: Proof. intros x y Hxy. apply not_EOlt_le. intros H. refine (isirrefl_EOlt _ _). refine (istrans_EOlt _ _ _ _ _). exact Hxy. exact H. Qed.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.QuotientSet UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders UniMath.Algebra.BinaryOperations UniMath.Algebra.Apartness UniMath.OrderTheory.Lattice.Lattice