Definition transport_one_cell_FlFr_iso {C : bicat} {A : Type} (f g : A -> C) {a₁ a₂ : A} (p : a₁ = a₂) (h : C⟦f a₁,g a₁⟧) : is_invertible_2cell (transport_one_cell_FlFr f g p h). Proof. refine (transport_one_cell_FlFr_inv f g p h ,, _). split ; cbn. - induction p ; cbn. rewrite <- !vassocr. rewrite !(maponpaths (λ z, _ • z) (vassocr _ _ _)). rewrite linvunitor_lunitor, id2_left. apply rinvunitor_runitor. - induction p ; cbn. rewrite <- !vassocr. rewrite !(maponpaths (λ z, _ • z) (vassocr _ _ _)). rewrite runitor_rinvunitor, id2_left. apply lunitor_linvunitor. Defined.
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.