proposition: Lemma plusNonnegativeReals_eqcompat_l : ∏ x y z: NonnegativeReals, (y + x = z + x) <-> (y = z).
proof: Proof. intros x y z ; split. - intro H ; apply isantisymm_leNonnegativeReals ; split. + apply_pr2 (plusNonnegativeReals_lecompat_l x). rewrite H ; refine (isrefl_leNonnegativeReals _). + apply_pr2 (plusNonnegativeReals_lecompat_l x). rewrite H ; refine (isrefl_leNonnegativeReals _). - now intros ->. 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