Definition transposition_mat_rows {X : UU} {m n : nat} (i j : ⟦ m ⟧%stn) : (Matrix X m n) -> Matrix X m n. Proof. intros mat k. destruct (stn_eq_or_neq i k). - apply (mat j). - destruct (stn_eq_or_neq j k). + exact (mat i). + exact (mat k). 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.