Lemma isldistr_minus_multNonnegativeReals : ∏ x y z : NonnegativeReals, z * (x - y) = z * x - z * y. Proof. intros x y z. apply plusNonnegativeReals_eqcompat_l with (Dcuts_mult z y). rewrite <- isldistr_plus_multNonnegativeReals, <- !maxNonnegativeReals_minus_plus. apply isldistr_max_multNonnegativeReals. 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.