proposition: Lemma isldistr_minus_multNonnegativeReals : ∏ x y z : NonnegativeReals, z * (x - y) = z * x - z * y.
proof: 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.
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