Definition binprod_psfunctor_invertible_2cells : invertible_cells binprod_psfunctor_data. Proof. split ; cbn. - intros b. is_iso. + use binprod_ump_2cell_invertible. * is_iso. * is_iso. + use binprod_ump_2cell_invertible. * is_iso. ** apply property_from_invertible_2cell. ** apply psfunctor_id. * is_iso. ** apply property_from_invertible_2cell. ** apply psfunctor_id. - intros b₁ b₂ b₃ f g. is_iso. + apply pair_1cell_comp_invertible. + use binprod_ump_2cell_invertible. * is_iso. ** apply property_from_invertible_2cell. ** apply psfunctor_comp. * is_iso. ** apply property_from_invertible_2cell. ** apply psfunctor_comp. 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.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Constant. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Limits.Final. Require Import UniMath.Bicategories.Limits.Products. Import Products.Notations.