Proposition mon_lassociator_pr2 (x y z : M) : mon_lassociator x y z · semi_cart_tensor_pr2 M_cart x (y ⊗ z) = semi_cart_tensor_pr2 M_cart x y #⊗ identity _. Proof. unfold semi_cart_tensor_pr2. rewrite <- tensor_id_id. rewrite !assoc. rewrite <- tensor_lassociator. rewrite !assoc'. rewrite mon_lunitor_triangle. rewrite !tensor_comp_id_r. apply idpath. 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.Adjunctions.Core. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Import BifunctorNotations. Import MonoidalNotations.