Definition is_cartesian_from_factor {B : bicat} {e b : B} {p : e --> b} {x : B} {f₁ f₂ g : x --> e} (α : f₁ ==> f₂) (Hα : is_invertible_2cell α) (β : f₁ ==> g) (γ : f₂ ==> g) (Hγ : is_cartesian_2cell_sfib p γ) (q : β = α • γ) : is_cartesian_2cell_sfib p β. Proof. use (is_cartesian_eq _ (!q)). use vcomp_is_cartesian_2cell_sfib. - apply invertible_is_cartesian_2cell_sfib. exact Hα. - exact Hγ. 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.