proposition: Lemma EOlt_noteq : ∏ x y : X, x < y -> x != y.
proof: Proof. intros x y Hgt Heq. rewrite Heq in Hgt. now apply isirrefl_EOgt in Hgt. 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