Definition binprod_cocone_has_binprod_ump_1_one_types : bincoprod_ump_1 (bincoprod_cocone_one_types X Y). Proof. intros Z. use make_bincoprod_1cell. - cbn ; intro z. induction z as [ x | y ]. + exact (bincoprod_cocone_inl Z x). + exact (bincoprod_cocone_inr Z y). - use make_invertible_2cell. + intro ; apply idpath. + apply one_type_2cell_iso. - use make_invertible_2cell. + intro ; apply idpath. + apply one_type_2cell_iso. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.OneTypes. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Examples.MorphismsInOneTypes. Require Import UniMath.Bicategories.Limits.CommaObjects. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.PullbackFunctions. Require Import UniMath.Bicategories.Limits.Examples.OneTypesLimits. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Colimits.Coproducts. Require Import UniMath.Bicategories.Colimits.Extensive.