Lemma whisker_r_eq {W X Y Z : C} {f : C⟦Y,Z⟧} {g : C⟦X,Y⟧} (k₁ k₂ : C⟦Z,W⟧) (α β : k₁ ==> k₂) : α ▻ f = β ▻ f -> α ▻ (f ∘ g) = β ▻ (f ∘ g). Proof. intros Hαβ. rewrite !lwhisker_hcomp. rewrite !lwhisker_hcomp in Hαβ. rewrite <- !hcomp_identity. apply (vcomp_lcancel (lassociator _ _ _)). { is_iso. } rewrite <- !hcomp_lassoc. rewrite Hαβ. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors.