proposition: Lemma Dcuts_inv_in : ∏ x, (0 < x)%NRat -> X x -> (Dcuts_inv_val (/ x)%NRat) -> empty.
proof: 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.
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