proposition: Lemma plusNonnegativeRationals_lt_le_ltcompat : ∏ x x' y y' : NonnegativeRationals, x < x' -> y <= y' -> x + y < x' + y'.
proof: Proof. intros x x' y y' Hx Hy. apply istrans_le_lt_ltNonnegativeRationals with (x + y'). - now apply hqlehandplusl, Hy. - now apply hqlthandplusr, Hx. Qed.
imports: UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders UniMath.RealNumbers.Sets UniMath.RealNumbers.Fields UniMath.Algebra.DivisionRig UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim