Lemma prev_nat (n : nat) (p : n > 0): ∑ m, S m = n. Proof. destruct n as [| n]. { contradiction (negnatlthn0 _ p). } exists n; reflexivity. Defined.
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.