Definition ver_sq_weq_ver_locally_univalent {B : verity_double_bicat} (H : vertically_saturated B) : ver_locally_univalent B ≃ ver_sq_locally_univalent B := (weqonsecfibers _ _ (λ x, weqonsecfibers _ _ (λ y, is_univalent_hom_v_weq_is_univalent_hom_v_sq H x y)) ∘ is_univalent_2_1_weq_local_univ (ver_bicat_of_verity_double_bicat B))%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.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.