Definition corestrict_full_image_weak_equivalence (B₁_is_univalent_2_1 : is_univalent_2_1 B₁) (B₂_is_univalent_2_1 : is_univalent_2_1 B₂) (FI_is_univalent_2_1 : is_univalent_2_1 (full_image F)) (F_local_equiv : local_equivalence B₁_is_univalent_2_1 B₂_is_univalent_2_1 F) : weak_equivalence B₁_is_univalent_2_1 FI_is_univalent_2_1 corestrict_full_image. Proof. split. - exact (corestrict_full_image_local_equivalence _ _ _ F_local_equiv). - apply corestrict_full_image_essentially_surjective. 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.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Examples.Image. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Properties.