Lemma le0_NonnegativeReals : ∏ x : NonnegativeReals, (x <= 0) <-> (x = 0). Proof. intros x ; split ; intros Hx. - apply isantisymm_leNonnegativeReals. split. + exact Hx. + apply isnonnegative_NonnegativeReals. - rewrite Hx. apply isrefl_leNonnegativeReals. Qed.
Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.NonnegativeRationals.