Definition hor_left_adjoint_equivalence_weq_gregarious_equivalence (HB_2_1 : locally_univalent_verity_double_bicat B) (H : weakly_hor_invariant B) (H' : vertically_saturated B) {x y : B} (h : x --> y) : left_adjoint_equivalence h ≃ ∑ (v : x -|-> y), is_gregarious_equivalence h v := (is_hor_gregarious_equivalence_weq_is_gregarious_equivalence h ∘ hor_left_adjoint_equivalence_weq_hor_gregarious_equivalence HB_2_1 H H' h)%weq.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.UnderlyingCats. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.CellsAndSquares. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.LocalUnivalence. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.CompanionPairs. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.CompanionPairUnique. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.CompanionPairAdjEquiv.