Definition street_fib_is_internal_sfib_cleaving : internal_sfib_cleaving F. Proof. intros C₀ G₁ G₂ α. simple refine (_ ,, _ ,, _ ,, _ ,, _). - exact (street_fib_is_internal_sfib_cleaving_lift α). - exact (street_fib_is_internal_sfib_cleaving_lift_mor α). - exact (street_fib_is_internal_sfib_cleaving_lift_over α). - exact (street_fib_is_internal_sfib_cleaving_lift_cartesian α). - abstract (use nat_trans_eq ; [ apply homset_property | ] ; intro x ; cbn ; exact (pr122 (HF (pr1 G₂ x) (pr1 G₁ x) (pr1 α x)))). 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.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.DisplayedCats.StreetFibration. Require Import UniMath.CategoryTheory.DisplayedCats.StreetOpFibration. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration.