Definition assoc_right_tensor_m : ∏ x1 x2 x3 x4 : C, D⟦H (assoc_right TC ((x1, TC (x2, x3)), x4)) , assoc_right TD ((H x1, TD (H x2, H x3)), H x4)⟧. Proof. do 4 intro. use (_ · _). 3: { use (# (assoc_right TD)). 2: { use catbinprodmor. 4: apply identity. 2: { use catbinprodmor. 3: apply identity. 2: apply (nat_z_iso_inv (TransportedTensorComm Duniv H_eso H_ff TC) (x2,x3)). } } } exact (nat_z_iso_inv TransportedAssocRight ((x1,TC (x2,x3)),x4)). 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.