Definition transposition_fun {n : nat} (i j : ⟦ n ⟧%stn) : ⟦ n ⟧%stn -> ⟦ n ⟧%stn. Proof. intros k. destruct (stn_eq_or_neq i k). - exact j. - destruct (stn_eq_or_neq j k). + exact i. + exact 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.