Lemma monoidal_pointed_objects_disp_tensor_data_aux1 (v w w' : V) (g : V ⟦ w, w' ⟧) (pv : cosliced v) (pw : cosliced w) (pw' : cosliced w') (Hypg : pw · g = pw') : luinv^{ Mon_V }_{ I_{ Mon_V}} · pv ⊗^{ Mon_V} pw · v ⊗^{ Mon_V}_{l} g = luinv^{ Mon_V }_{ I_{ Mon_V}} · pv ⊗^{ Mon_V} pw'. Proof. rewrite assoc'. apply maponpaths. rewrite <- Hypg. unfold functoronmorphisms1. rewrite assoc'. apply maponpaths. apply pathsinv0, (bifunctor_leftcomp 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.