Definition make_binprod_ump (υ₁ : binprod_ump_1) (υ₂ : has_binprod_ump_2_cell) (υ₂pr1 : has_binprod_ump_2_cell_pr1 υ₂) (υ₂pr2 : has_binprod_ump_2_cell_pr2 υ₂) (υ₃ : has_binprod_ump_2_cell_unique) : has_binprod_ump. Proof. split. - exact υ₁. - intros q f₁ f₂ α β. use iscontraprop1. + abstract (use invproofirrelevance ; intros φ₁ φ₂ ; use subtypePath ; [ intro ; apply isapropdirprod ; apply cellset_property | ] ; exact (υ₃ q f₁ f₂ α β (pr1 φ₁) (pr1 φ₂) (pr12 φ₁) (pr22 φ₁) (pr12 φ₂) (pr22 φ₂))). + simple refine (_ ,, _ ,, _). * exact (υ₂ q f₁ f₂ α β). * abstract (apply υ₂pr1). * abstract (apply υ₂pr2). 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.