proposition: Lemma le0_NonnegativeReals : ∏ x : NonnegativeReals, (x <= 0) <-> (x = 0).
proof: Proof. intros x ; split ; intros Hx. - apply isantisymm_leNonnegativeReals. split. + exact Hx. + apply isnonnegative_NonnegativeReals. - rewrite Hx. apply isrefl_leNonnegativeReals. 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