Proposition make_pstrans_from_cat_laws : is_pstrans make_pstrans_from_cat_data. Proof. repeat split. - cbn ; intros x y f g p. induction p. etrans. { apply maponpaths_2. apply maponpaths. refine (_ @ psfunctor_id2 G f). apply maponpaths. apply homset_property. } rewrite lwhisker_id2. rewrite id2_left. refine (!_). etrans. { do 2 apply maponpaths. refine (_ @ psfunctor_id2 F f). apply maponpaths. apply homset_property. } rewrite id2_rwhisker. rewrite id2_right. apply idpath. - exact τid. - exact τc. Qed.
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.