proposition: Lemma istrans_Dcuts_le_lt_rel : ∏ x y z : Dcuts_set, Dcuts_le_rel x y -> Dcuts_lt_rel y z -> Dcuts_lt_rel x z.
proof: Proof. intros x y z Hle. apply hinhfun ; intros r. exists (pr1 r) ; split. - intros Xr ; apply (pr1 (pr2 r)). now refine (Hle _ _). - exact (pr2 (pr2 r)). Qed.
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.RealNumbers.Sets UniMath.Algebra.ConstructiveStructures UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim UniMath.RealNumbers.NonnegativeRationals