Definition lift_2cell_factor_type {c : B} {cc : D c} {h h' : c --> a} {gg : cc -->[ h · f ] bb} {gg' : cc -->[ h' · f ] bb} {δ : h ==> h'} (σσ : gg ==>[ δ ▹ f] gg') (Lh : lift_1cell_factor gg) (Lh' : lift_1cell_factor gg') : UU := ∑ (δδ : Lh ==>[ δ ] Lh'), transportf (λ z, _ ==>[ z ] _) (id2_right _ @ ! id2_left _ ) (δδ ▹▹ ff •• disp_cell_lift_1cell_factor Lh') = disp_cell_lift_1cell_factor Lh •• σσ.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles.