Definition assoc_left_tensor_l : ∏ x1 x2 x3 x4 : C, D⟦assoc_left TD ((TD (H x1, H x2), H x3), H x4) , H (assoc_left TC ((TC (x1, x2), x3), x4))⟧. Proof. do 4 intro. use (_ · _). 3: apply TransportedAssocLeft. use (# TD). use catbinprodmor. 2: apply identity. use (# TD). use catbinprodmor. 1: exact ((TransportedTensorComm Duniv H_eso H_ff TC) (x1,x2)). apply identity. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.catiso. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.PrecompEquivalence. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.TotalCategoryFacts. Require Import UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensor. Require Import UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensorUnit.