Definition id_is_cartesian_2cell_sfib {B : bicat} {e b : B} (p : e --> b) {x : B} (f : x --> e) : is_cartesian_2cell_sfib p (id2 f). Proof. intros g α δp q. use iscontraprop1. - abstract (use invproofirrelevance ; intros φ₁ φ₂ ; use subtypePath ; [ intro ; apply isapropdirprod ; apply cellset_property | ] ; exact (!(id2_right _) @ pr22 φ₁ @ !(pr22 φ₂) @ id2_right _)). - refine (α ,, _ ,, _). + abstract (rewrite q ; rewrite id2_rwhisker ; apply id2_right). + abstract (apply id2_right). 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.