Lemma whiskering_on_both_sides_with_lunitor_left_unit (x y : V) : monoidal_unit V ⊗^{V}_{l} (mon_lunitor x ⊗^{V}_{r} y) = monoidal_unit V ⊗^{V}_{l} mon_lassociator _ _ _ · (mon_rassociator _ _ (x ⊗ y) · mon_lunitor _ ⊗^{V}_{r} (x ⊗ y)). Proof. refine (Categories.right_whisker_with_lunitor' _ _ _ @ _). rewrite (bifunctor_leftcomp V). apply maponpaths. refine (_ @ mon_lunitor_triangle_transposed _). exact (leftwhisker_of_lunitor_with_unit (x ⊗ y)). Qed.
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.Isos. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import MonoidalNotations.