Proposition cancel_braiding {a x y : V} (f g : a --> x ⊗ y) : (f · sym_mon_braiding _ _) = (g · sym_mon_braiding _ _) -> f = g. Proof. intros e. transitivity (f · sym_mon_braiding _ _ · sym_mon_braiding _ _). { rewrite <- assoc, sym_mon_braiding_inv, id_right. reflexivity. } rewrite e. rewrite <- assoc, sym_mon_braiding_inv, id_right. reflexivity. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Import MonoidalNotations.