Definition cod_invertible_is_cartesian_2cell {c₁ c₂ : B} {s₁ s₂ : c₁ --> c₂} {α : s₁ ==> s₂} {t₁ : cod_disp_bicat B c₁} {t₂ : cod_disp_bicat B c₂} {ss₁ : t₁ -->[ s₁ ] t₂} {ss₂ : t₁ -->[ s₂ ] t₂} (αα : ss₁ ==>[ α ] ss₂) (Hαα : is_invertible_2cell (pr1 αα)) : is_cartesian_2cell (cod_disp_bicat B) αα. Proof. apply is_cartesian_2cell_sfib_to_is_cartesian_2cell. apply invertible_is_cartesian_2cell_sfib. exact Hαα. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Core.Examples.OneTypes. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Codomain. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.Examples.OneTypesLimits.