Definition one_types_universal_coprod_map_idpath (W : @bincoprod_cocone ∁ (hfp_HLevel 3 (bincoprod_cocone_inl (pr1 (bincoprod_of ∁ X Y))) h) (hfp_HLevel 3 (bincoprod_cocone_inr (pr1 (bincoprod_of ∁ X Y))) h)) (z : pr1 Z) (q : pr1 X ⨿ pr1 Y) (p : h z = q) : one_types_universal_coprod_map W z q p = one_types_universal_coprod_map W z (h z) (idpath _). Proof. induction p. 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.