Lemma isinvolutive_invNonnegativeRationals : ∏ x, / / x = x. Proof. intros x. generalize (eq0orgt0NonnegativeRationals x) ; apply sumofmaps ; intro Hx0. - now rewrite Hx0, !inv_zeroNonnegativeRationals. - apply (multNonnegativeRationals_eqcompat_l (/ x)). + apply ispositive_invNonnegativeRationals ; exact Hx0. + rewrite islinv_NonnegativeRationals, isrinv_NonnegativeRationals. * reflexivity. * apply ispositive_invNonnegativeRationals ; exact Hx0. * exact Hx0. 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.