Lemma Dcuts_inv_in : ∏ x, (0 < x)%NRat -> X x -> (Dcuts_inv_val (/ x)%NRat) -> empty. Proof. intros x Hx0 Xx. unfold neg ; apply (hinhuniv (P := make_hProp _ isapropempty)) ; intros l. set (H := pr1 (pr2 l) _ Xx). rewrite islinv_NonnegativeRationals in H. - apply (pr2 (notlt_geNonnegativeRationals _ _)) in H. now apply H, (pr2 (pr2 (pr2 l))). - exact Hx0. 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.