Definition disp_locally_groupoid_over_id {B : bicat} (D : disp_bicat B) : UU := ∏ (a b : B) (f : B ⟦ a, b ⟧) (aa : D a) (bb : D b) (ff gg : aa -->[ f] bb) (xx : disp_2cells (id2_invertible_2cell f) ff gg), is_disp_invertible_2cell (is_invertible_2cell_id₂ f) xx.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.