Lemma cell_transportb_to_f {a b : C} {f g : C⟦a,b⟧} {α β : f ==> g} {e : α = β} {aa : D a} {bb : D b} {ff : aa -->[f] bb} {gg : aa -->[g] bb} {αα : ff ==>[α] gg} {ββ : ff ==>[β] gg} (ee : αα = cell_transportb e ββ) : cell_transportf e αα = ββ. Proof. apply cell_transportf_pathsinv0. apply pathsinv0. exact ee. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.