proposition: Lemma id_mat_ij {n : nat} (i j : ⟦ n ⟧%stn) : i ≠ j -> (@identity_matrix R n) i j = rigunel1.
proof: Proof. intros i_neq_j. unfold identity_matrix. now rewrite (stn_eq_or_neq_right i_neq_j). 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