Lemma lunitor_natural (a b : C) (f g : C ⟦ a, b ⟧) (x : f ==> g) : id2 (identity a) ⋆ x • lunitor g = lunitor f • x. Proof. unfold hcomp. rewrite <- vassocr. rewrite vcomp_lunitor. rewrite vassocr. apply maponpaths_2. rewrite id2_rwhisker. apply id2_left. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.