Proposition psfunctor_to_indexed_cat_laws : indexed_cat_laws psfunctor_to_indexed_cat_data. Proof. repeat split. - intros x y f xx. pose (p := nat_trans_eq_pointwise (psfunctor_lunitor F f) xx). cbn in p ; cbn. refine (p @ _) ; clear p. rewrite !assoc'. do 2 apply maponpaths. refine (psfunctor_idtoiso _ _ @ _). do 3 apply maponpaths. apply homset_property. - intros x y f xx. pose (p := nat_trans_eq_pointwise (psfunctor_runitor F f) xx). cbn in p ; cbn. refine (p @ _) ; clear p. rewrite !assoc'. do 2 apply maponpaths. refine (psfunctor_idtoiso _ _ @ _). do 3 apply maponpaths. apply homset_property. - intros w x y z f g h ww. pose (p := nat_trans_eq_pointwise (psfunctor_lassociator F f g h) ww). cbn in p ; cbn. rewrite id_left in p. refine (_ @ p) ; clear p. apply maponpaths. refine (!_). refine (psfunctor_idtoiso _ _ @ _). do 3 apply maponpaths. apply homset_property. 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.IndexedCategories.IndexedCategory. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.OppositeCategory.Core. 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. Section PseudoFunctorFromCat. End PseudoFunctorFromCat.