proposition: Lemma TransportedAssocRight : nat_z_iso (HHH ∙ assoc_right TD) (assoc_right TC ∙ H).
proof: Proof. use nat_z_iso_comp. 2: apply nat_z_iso_functor_comp_assoc. use nat_z_iso_comp. 2: { use post_whisker_nat_z_iso. 2: exact unassoc_commutes. } use nat_z_iso_comp. 2: apply (nat_z_iso_inv (nat_z_iso_functor_comp_assoc _ _ _)). use nat_z_iso_comp. 3: apply nat_z_iso_functor_comp_assoc. apply pre_whisker_nat_z_iso. use nat_z_iso_comp. 3: apply nat_z_iso_functor_comp_assoc. use nat_z_iso_comp. 3: { apply pre_whisker_nat_z_iso. apply TransportedTensorComm. } use nat_z_iso_comp. 3: apply (nat_z_iso_inv (nat_z_iso_functor_comp_assoc _ _ _)). use nat_z_iso_comp. 2: apply nat_z_iso_functor_comp_assoc. apply post_whisker_nat_z_iso. use product_of_commuting_squares. { apply (make_nat_z_iso _ _ _ (is_nat_z_iso_nat_trans_id H)). } apply TransportedTensorComm. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.catiso UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.PrecompEquivalence UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.TotalCategoryFacts UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensor UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensorUnit