Definition eso_ff_is_equiv : left_equivalence e. Proof. simple refine ((_ ,, (_ ,, _)) ,, (_ ,, _)). - exact (is_eso_lift_1 _ He₁ He₂ (id₁ _) (id₁ _) α). - exact (inv_of_invertible_2cell (is_eso_lift_1_comm_left _ He₁ He₂ (id₁ _) (id₁ _) α)). - exact ((is_eso_lift_1_comm_right _ He₁ He₂ (id₁ _) (id₁ _) α)). - apply property_from_invertible_2cell. - apply property_from_invertible_2cell. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. 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.AdjointUnique. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.Eso. Require Import UniMath.Bicategories.Limits.Pullbacks.