proposition: 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: Proof. rewrite assoc'. apply maponpaths. rewrite <- Hypg. unfold functoronmorphisms1. rewrite assoc'. apply maponpaths. apply pathsinv0, (bifunctor_leftcomp Mon_V). Qed.
imports: UniMath.MoreFoundations.All UniMath.Foundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Projection UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.coslicecat