Lemma monoidal_pointed_objects_disp_tensor_data_aux2 (v v' w : V) (f : V ⟦ v, v' ⟧) (pv : cosliced v) (pv' : cosliced v') (pw : cosliced w) (Hypf : pv · f = pv') : luinv^{ Mon_V }_{ I_{ Mon_V}} · pv ⊗^{ Mon_V} pw · f ⊗^{ Mon_V}_{r} w = luinv^{ Mon_V }_{ I_{ Mon_V}} · pv' ⊗^{ Mon_V} pw. Proof. rewrite assoc'. apply maponpaths. rewrite <- Hypf. do 2 rewrite (bifunctor_equalwhiskers Mon_V). unfold functoronmorphisms2. rewrite assoc'. apply maponpaths. apply pathsinv0, (bifunctor_rightcomp Mon_V). Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Foundations.PartA. 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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.coslicecat. Import BifunctorNotations. Import MonoidalNotations.