Proposition copy_assoc (x : C) : copy x · (copy x #⊗ identity _) = copy x · (identity _ #⊗ copy x) · mon_rassociator _ _ _. Proof. rewrite copy_assoc'. rewrite !assoc'. rewrite mon_lassociator_rassociator. rewrite id_right. 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.