Lemma isassoc_Dcuts_min : ∏ x y z : Dcuts, Dcuts_min (Dcuts_min x y) z = Dcuts_min x (Dcuts_min y z). Proof. intros x y z. apply Dcuts_eq_is_eq ; intros r. split ; intros Hr ; repeat split. - apply (pr1 (pr1 Hr)). - apply (pr2 (pr1 Hr)). - apply (pr2 Hr). - apply (pr1 Hr). - apply (pr1 (pr2 Hr)). - apply (pr2 (pr2 Hr)). Qed.
Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.NonnegativeRationals.