Lemma eq0orgt0NonnegativeRationals : ∏ x : NonnegativeRationals, (x = 0) ⨿ (0 < x). Proof. intros x. generalize (le_eqorltNonnegativeRationals 0 x (pr2 x)) ; apply sumofmaps ; intros Hx. - rewrite Hx ; now left. - right ; exact Hx. 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.