Definition make_is_classifying_full (H : is_classifying_full_help) : is_classifying_full. Proof. intros x f g β. specialize (H x f g β). refine (pr1 H ,, _). use (isotoid_2_1 (pr1 (is_discrete_disp_map_slice HB (discrete_sopfib_subbicat_props B HB) (discrete_sopfib_disp_map_bicat_in_discrete B) x))). use make_invertible_2cell. - refine (pr12 H ,, _). abstract (cbn ; use vcomp_move_R_pM ; [ is_iso | ] ; cbn ; exact (pr222 H)). - apply is_invertible_2cell_in_disp_map_slice_bicat ; cbn. exact (pr122 H). 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.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.Discreteness. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.Properties.ClosedUnderPullback. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayMapBicatSlice. Require Import UniMath.Bicategories.Logic.DisplayMapBicat. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.PullbackFunctions. Import PullbackFunctions.Notations.