Proposition sym_mon_braiding_proj2 {x y : C} : sym_mon_braiding _ x y · proj2 = proj1. Proof. unfold proj2. rewrite !assoc. rewrite <- tensor_sym_mon_braiding. rewrite !assoc'. rewrite sym_mon_braiding_lunitor. reflexivity. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal. Import MonoidalNotations.