Definition binprod_cocone_has_binprod_ump_2_one_types : bincoprod_ump_2 (bincoprod_cocone_one_types X Y). Proof. intros Z φ ψ α β. use iscontraprop1. - abstract (use invproofirrelevance ; intros γ₁ γ₂ ; use subtypePath ; [ intro ; apply isapropdirprod ; apply cellset_property | ] ; use funextsec ; intro z ; induction z as [ x | y ] ; [ exact (eqtohomot (pr12 γ₁) x @ !(eqtohomot (pr12 γ₂) x)) | exact (eqtohomot (pr22 γ₁) y @ !(eqtohomot (pr22 γ₂) y)) ]). - simple refine (_ ,, _ ,, _). + cbn ; intro z. induction z as [ x | y ]. * exact (α x). * exact (β y). + abstract (use funextsec ; intro z ; cbn ; apply idpath). + abstract (use funextsec ; intro z ; cbn ; apply idpath). 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.