Definition section_to_psfunctor_invertible_cells : invertible_cells section_to_psfunctor_data. Proof. split. - intro x ; cbn. use is_invertible_disp_to_total. simple refine (_ ,, _). + apply is_invertible_2cell_id₂. + exact (pr2 (section_on_id s x)). - intros x y z f g ; cbn. use is_invertible_disp_to_total. simple refine (_ ,, _). + apply is_invertible_2cell_id₂. + exact (pr2 (section_on_comp s f g)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. 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.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor.