Definition pb_ump_2_grpds_iso_comma : pb_ump_2 (grpds_iso_comma_pb_cone F G). Proof. intros C φ ψ α β r. use iscontraprop1. - abstract (use invproofirrelevance ; intros τ₁ τ₂ ; use subtypePath ; [ intro ; apply isapropdirprod ; apply cellset_property | ] ; use subtypePath ; [ intro ; apply isapropunit | ] ; exact (iso_comma_ump_eq _ _ _ _ _ _ (maponpaths pr1 (pr12 τ₁)) (maponpaths pr1 (pr22 τ₁)) (maponpaths pr1 (pr12 τ₂)) (maponpaths pr1 (pr22 τ₂)))). - simple refine (_ ,, _). + exact (pb_ump_2_grpds_nat_trans φ ψ α β r). + split. * exact (pb_ump_2_grpds_nat_trans_pr1 φ ψ α β r). * exact (pb_ump_2_grpds_nat_trans_pr2 φ ψ α β r). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.IsoCommaCategory. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.Groupoids. Require Import UniMath.Bicategories.Limits.Pullbacks.