Definition is_cartesian_2cell_sfib_inv2cell {B : bicat} {x e b : B} {p p' : e --> b} (α : invertible_2cell p p') {f g : x --> e} {β : f ==> g} (Hβ : is_cartesian_2cell_sfib p β) : is_cartesian_2cell_sfib p' β. Proof. intros k ζ δp q. use iscontraprop1. - exact (is_cartesian_2cell_sfib_factor_inv2cell_unique α Hβ δp q). - simple refine (_ ,, _ ,, _). + exact (is_cartesian_2cell_sfib_factor_inv2cell α Hβ δp q). + exact (is_cartesian_2cell_sfib_factor_inv2cell_over α Hβ δp q). + apply is_cartesian_2cell_sfib_factor_comm. Defined.
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.