Lemma col_vec_inj_pointwise { X : rig } { n : nat } (v1 v2 : Vector X n) : forall i : (stn n), (col_vec v1 i) = (col_vec v2 i) -> (v1 i) = (v2 i). Proof. intros i eq; apply (invmaponpathsweq (@weq_vector_1 X) _ _ eq). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. 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.Domains_and_Fields. Require Import UniMath.Algebra.GaussianElimination.Auxiliary. Require Import UniMath.Algebra.GaussianElimination.Vectors.