Definition isBinCoproduct_in_iso_comma : isBinCoproduct (iso_comma F G) x y z i₁ i₂. Proof. intros w f g. use iscontraprop1. - exact (isBinCoproduct_in_iso_comma_unique f g). - simple refine (_ ,, _ ,, _). + exact (isBinCoproduct_in_iso_comma_ump f g). + exact (isBinCoproduct_in_iso_comma_ump_in1 f g). + exact (isBinCoproduct_in_iso_comma_ump_in2 f g). 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.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.IsoCommaCategory. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Preservation.