Definition pb_ump_2_grpds_nat_trans : φ ==> ψ. Proof. refine (_ ,, tt). use (iso_comma_ump2 _ _ _ _ (pr1 α) (pr1 β)). abstract (intros x ; pose (nat_trans_eq_pointwise (maponpaths pr1 r) x) as z ; cbn in z ; unfold iso_comma_commute_nat_trans_data in z ; rewrite !id_left, !id_right in z ; exact z). 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.