Lemma vecsum_zero {n} : Σ (@const_vec R n 0%rig) = 0%rig. Proof. induction n as [ | n IH]. { reflexivity. } rewrite vecsum_step. rewrite rigrunax1. apply IH. Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Nat. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.Vectors. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Algebra.Matrix. Require Import UniMath.Algebra.GaussianElimination.Auxiliary.