Proposition is_deterministic_sym_mon_braiding (x y : C) : is_deterministic (sym_mon_braiding _ x y). Proof. unfold is_deterministic. rewrite <- !copy_tensor. etrans. { rewrite !assoc. rewrite <- tensor_sym_mon_braiding. rewrite !assoc'. apply idpath. } rewrite !assoc'. apply maponpaths. rewrite inner_swap_commute_with_swap. 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. Require Import UniMath.CategoryTheory.MarkovCategories.MarkovCategory. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Import MonoidalNotations. Import BifunctorNotations.