proposition: Lemma plusNonnegativeReals_apcompat_r : ∏ x y z: NonnegativeReals, (y ≠ z) <-> (x + y ≠ x + z).
proof: Proof. intros x y z. rewrite ! (iscomm_plusNonnegativeReals x). now apply plusNonnegativeReals_apcompat_l. 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