Proposition pairing_sym_mon_braiding {a x y : C} (f : a --> x) (g : a --> y) : ⟨f,g⟩ · sym_mon_braiding _ _ _ = ⟨g,f⟩. Proof. unfold pairing. rewrite <- assoc. rewrite tensor_sym_mon_braiding. rewrite assoc. rewrite copy_comm. 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.