Definition vcomp_is_cartesian_2cell_sfib : is_cartesian_2cell_sfib p (α • β). Proof. intros k ζ δp q. use iscontraprop1. - apply vcomp_is_cartesian_2cell_sfib_unique. exact q. - simple refine (_ ,, _ ,, _). + simple refine (is_cartesian_2cell_sfib_factor _ Hα _ δp _). * simple refine (is_cartesian_2cell_sfib_factor _ Hβ ζ (δp • (α ▹ p)) _). abstract (rewrite !vassocl ; rewrite q ; rewrite <- rwhisker_vcomp ; apply idpath). * apply is_cartesian_2cell_sfib_factor_over. + apply is_cartesian_2cell_sfib_factor_over. + abstract (simpl ; rewrite !vassocr ; rewrite !is_cartesian_2cell_sfib_factor_comm ; apply idpath). 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.