Lemma transport_two_cell_FlFr {C : bicat} {A : Type} {X Y : C} (F G : A -> C⟦X,Y⟧) {a₁ a₂ : A} (p : a₁ = a₂) (α : F a₁ ==> G a₁) : transportf (λ z, F z ==> G z) p α = idtoiso_2_1 _ _ (maponpaths G p) o α o (idtoiso_2_1 _ _ (maponpaths F p))^-1. Proof. induction p ; cbn. rewrite id2_right, id2_left. 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.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.