Lemma switch_row_latter_row' {m n} (r1 r2 : ⟦ m ⟧%stn) (mat : Matrix R m n) (i : ⟦m⟧%stn) (e : i = r2) (j : ⟦n⟧%stn) : switch_row r1 r2 mat i j = mat r1 j. Proof. destruct e; apply switch_row_latter_row. 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.Matrix. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.GaussianElimination.Auxiliary. Require Import UniMath.Algebra.GaussianElimination.Vectors. Require Import UniMath.Algebra.GaussianElimination.Matrices.