Definition disp_depprod_bicat_disp_invertible_2cell_inv_map {a b : B} {f : B ⟦ a, b ⟧} {aa : disp_depprod_bicat a} {bb : disp_depprod_bicat b} (ff : aa -->[ f] bb) (gg : aa -->[ f] bb) : disp_invertible_2cell (id2_invertible_2cell f) ff gg → (∏ (i : I), disp_invertible_2cell (id2_invertible_2cell f) (ff i) (gg i)). Proof. intros x i. use tpair. - exact (pr1 x i). - exact (disp_depprod_bicat_disp_is_invertible_2cell_pr _ (pr2 x) i). 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.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.