Theorem nat_le_diff {n m : ℕ} (p : n ≤ m) : ∑ (k : ℕ), n + k = m. Proof. exists (m - n). rewrite natpluscomm. exact (minusplusnmm _ _ p). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA.