Lemma interchange {X Y Z : C} {f₁ g₁ h₁ : C⟦Y,Z⟧} {f₂ g₂ h₂ : C⟦X,Y⟧} (η₁ : f₁ ==> g₁) (η₂ : f₂ ==> g₂) (ε₁ : g₁ ==> h₁) (ε₂ : g₂ ==> h₂) : (ε₁ o η₁) ⋆⋆ (ε₂ o η₂) = (ε₁ ⋆⋆ ε₂) o (η₁ ⋆⋆ η₂). Proof. apply hcomp_vcomp. 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.