proposition: Lemma plusNonnegativeRationals_minus_r : ∏ q r : NonnegativeRationals, (r + q) - q = r.
proof: Proof. intros q r. change r with (pr1 r,,pr2 r). generalize (pr1 r) (pr2 r) (pr1 q) (pr2 q) ; intros r' Hr q' Hq. rewrite (minusNonnegativeRationals_correct _ _ (plusNonnegativeRationals_le_l _ _)). apply subtypePath_prop. simpl pr1. unfold hqminus. rewrite hqplusassoc. rewrite (hqpluscomm (pr1 q)). rewrite hqlminus. rewrite hqplusr0. reflexivity. 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