Definition transposition_perm {n : nat} (i j : ⟦ n ⟧%stn) : ⟦ n ⟧%stn ≃ ⟦ n ⟧%stn. Proof. exists (transposition_fun i j). use isweq_iso. - exact (transposition_fun i j). - apply toforallpaths, transposition_self_inverse. - apply toforallpaths, transposition_self_inverse. 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.