Lemma idmat_i_to_idvec {n : nat} (i : ⟦ n ⟧%stn) : (@identity_matrix R) i = (@stdb_vector R i). Proof. apply funextfun. intros j. apply funextfun. intros k. now destruct (stn_eq_or_neq j k). 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.