Lemma mon_lunitor_triangle_transposed (x : V) : mon_lunitor (monoidal_unit V ⊗_{V} x) = mon_rassociator I_{V} I_{V} x · mon_lunitor I_{V} ⊗^{V}_{r} x. Proof. rewrite <- (when_bifunctor_becomes_rightwhiskering V). etrans. 2: { apply maponpaths, mon_lunitor_triangle. } rewrite assoc. refine (! id_left _ @ _). apply maponpaths_2. apply pathsinv0. apply monoidal_associatorisolaw. 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.