Lemma rwhisker_lwhisker_CAT {A B C D : category} {F : [A, B]} {G H : [B, C]} {I : [C, D]} (α : [B, C]⟦G, H⟧) : lwhisker_CAT F (rwhisker_CAT I α) · lassociator_CAT _ _ _ = lassociator_CAT _ _ _ · rwhisker_CAT I (lwhisker_CAT F α). Proof. apply (nat_trans_eq D); intro c. cbn. rewrite id_left; apply id_right. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering.