Definition pstrans_from_cat_into_cat : pstrans F G. Proof. use make_pstrans_from_cat. - exact τ. - intros x y f. use nat_z_iso_to_invertible_2cell. exact (pstrans_from_cat_into_cat_data_nat τ f). - abstract (intros x ; use nat_trans_eq ; [ apply homset_property | ] ; intro xx ; cbn -[psfunctor_id] ; rewrite !id_left ; exact (pr1 Hτ x xx)). - abstract (intros x y z f g ; use nat_trans_eq ; [ apply homset_property | ] ; intro xx ; cbn -[psfunctor_comp] ; rewrite !id_left ; rewrite !id_right ; exact (pr2 Hτ x y z f g xx)). 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.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedCategory. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedFunctor. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Discreteness. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Examples.DiscreteBicat. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.PseudoFunctorsIntoCat. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Section PseudoTransFromCat. End PseudoTransFromCat.