Definition switch_row {m n} (r1 r2 : ⟦ m ⟧%stn) (mat : Matrix R m n) : Matrix R m n. Proof. intros i j. induction (stn_eq_or_neq i r1). - exact (mat r2 j). - induction (stn_eq_or_neq i r2). + exact (mat r1 j). + exact (mat i j). 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.