proposition: Lemma plusNonnegativeReals_le_ltcompat : ∏ x y z t : NonnegativeReals, x <= y -> z < t -> x + z < y + t.
proof: Proof. intros x y z t Hxy Hzt. eapply istrans_le_lt_ltNonnegativeReals, plusNonnegativeReals_ltcompat_r, Hzt. now apply plusNonnegativeReals_lecompat_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