Lemma identity_matrix_symmetric {n : nat} : is_symmetric_mat (@identity_matrix R n). Proof. unfold is_symmetric_mat. apply funextfun. intros i. apply funextfun. intros j. unfold identity_matrix, transpose, flip. apply stn_eq_or_neq_symm_nondep. 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.