Lemma evaluation_is_pstrans: is_pstrans evaluation_pstrans_data. Proof. repeat split. - intros A A' F F' α. apply (nat_trans_eq (homset_property _)). intro Gb. induction Gb as [G b]. cbn. do 2 rewrite functor_id. do 2 rewrite id_left. apply id_right. - intro A. apply (nat_trans_eq (homset_property _)). intro Gb. induction Gb as [G b]. cbn. do 5 rewrite id_left. rewrite id_right. apply pathsinv0, functor_id. - intros A1 A2 A3 F H. apply (nat_trans_eq (homset_property _)). intro Gb. induction Gb as [G b]. cbn. do 7 rewrite id_right. do 3 rewrite functor_id. rewrite id_left, id_right. apply pathsinv0, functor_id. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.UnitorsAndAssociatorsForEndofunctors. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Biadjunction. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.Modifications.Modification. Import Bicat.Notations.