Lemma whisker_l_eq {W X Y Z : C} {f : C⟦X,Y⟧} {g : C⟦Y,Z⟧} (k₁ k₂ : C⟦W,X⟧) (α β : k₁ ==> k₂) : f ◅ α = f ◅ β -> (g ∘ f) ◅ α = (g ∘ f) ◅ β. Proof. intros Hαβ. rewrite !rwhisker_hcomp. rewrite !rwhisker_hcomp in Hαβ. rewrite <- !hcomp_identity. apply (vcomp_rcancel (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.