Lemma eq_of_le_le {a b : nat} (le_a_b : a ≤ b) (le_b_a : b ≤ a) : a = b. Proof. destruct (natlehchoice _ _ le_a_b) as [lt_a_b | e_a_b]. 2: { assumption. } apply fromempty. eapply natlthtonegnatgeh; eassumption. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Combinatorics.Maybe. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.RigsAndRings.