Lemma TransportedAssocLeft : nat_z_iso (HHH ∙ assoc_left TD) (assoc_left TC ∙ H). Proof. use nat_z_iso_comp. 3: apply nat_z_iso_functor_comp_assoc. use nat_z_iso_comp. 2: apply nat_z_iso_functor_comp_assoc. use nat_z_iso_comp. 3: { apply pre_whisker_nat_z_iso. apply ((TransportedTensorComm Duniv H_eso H_ff _)). } use nat_z_iso_comp. 3: apply (nat_z_iso_inv (nat_z_iso_functor_comp_assoc _ _ _)). use (post_whisker_nat_z_iso _ TD). use nat_z_iso_comp. 3: apply PrecompEquivalence.nat_z_iso_pair. use nat_z_iso_comp. 2: apply pair_functor_composite. use pair_nat_z_iso. - apply TransportedTensorComm. - apply functor_commutes_with_id. 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.