proposition: Lemma identity_matrix_symmetric {n : nat} : is_symmetric_mat (@identity_matrix R n).
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.Vectors UniMath.Algebra.RigsAndRings UniMath.Algebra.IteratedBinaryOperations UniMath.Algebra.Matrix UniMath.Algebra.Domains_and_Fields UniMath.Algebra.GaussianElimination.Auxiliary UniMath.Algebra.GaussianElimination.Vectors