Lemma leftwhisker_of_lunitor_with_unit (x : V) : monoidal_unit V ⊗^{V}_{l} lu^{V}_{x} = lu^{V}_{monoidal_unit V ⊗ x}. Proof. refine (_ @ ! mon_lunitor_triangle_transposed x). use (z_iso_inv_to_left _ _ _ (mon_rassociator _ _ _ ,, mon_lassociator _ _ _ ,, _)). { split ; apply monoidal_associatorisolaw. } refine (monoidal_triangleidentity _ _ _ @ _). apply maponpaths. apply pathsinv0, unitors_coincide_on_unit. 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.