Definition const_prod_psfunctor_invertible_cells : invertible_cells const_prod_psfunctor_data. Proof. split. - intro y. apply is_invertible_2cell_inv. - intros y₁ y₂ y₃ f g ; cbn. is_iso. + apply binprod_ump_2cell_invertible. * is_iso. ** apply property_from_invertible_2cell. ** apply property_from_invertible_2cell. * is_iso. ** apply property_from_invertible_2cell. ** apply property_from_invertible_2cell. + apply binprod_ump_2cell_invertible. * is_iso. apply property_from_invertible_2cell. * is_iso. apply property_from_invertible_2cell. 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.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Limits.Products. Import Products.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations.