Lemma runitor_natural (a b : C) (f g : C ⟦ a, b ⟧) (x : f ==> g) : x ⋆ id2 (identity b) • runitor g = runitor f • x. Proof. rewrite hcomp_hcomp'. unfold hcomp'. rewrite <- vassocr. rewrite vcomp_runitor. rewrite vassocr. apply maponpaths_2. rewrite lwhisker_id2. 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.