Definition has_binprod_cat_ump_binprod_ump_1_pr2 : invertible_2cell (has_binprod_cat_ump_binprod_ump_1_mor · binprod_cone_pr2 p) (binprod_cone_pr2 q). Proof. apply z_iso_to_inv2cell. exact (pr2 (category_binproduct_z_iso_inv _ _ (nat_z_iso_pointwise_z_iso (invertible_2cell_to_nat_z_iso _ _ (left_equivalence_counit_iso (H (pr1 q)))) (binprod_cone_pr1 q ,, binprod_cone_pr2 q)))). 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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. 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.Unitors. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Univalence.