Definition internal_sfib_cleaving : UU := ∏ (x : B) (f : x --> b) (g : x --> e) (α : f ==> g · p), ∑ (h : x --> e) (γ : h ==> g) (β : invertible_2cell (h · p) f), is_cartesian_2cell_sfib γ × γ ▹ p = β • α.
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.DisplayedCats.StreetFibration. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence.