proposition: Lemma istrans_EOlt_le: ∏ x y z : X, x < y -> y <= z -> x < z.
proof: Proof. exact (pr1 (pr2 (pr2 (pr2 (pr2 (pr2 X)))))). 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