Lemma plusNonnegativeRationals_eqcompat_l: ∏ k x y : NonnegativeRationals, (k + x = k + y) -> (x = y). Proof. intros k x y H. apply isantisymm_leNonnegativeRationals ; apply_pr2 (plusNonnegativeRationals_lecompat_l k) ; rewrite H ; apply isrefl_leNonnegativeRationals. Qed.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.Fields. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim.