proposition: Proposition psfunctor_to_indexed_cat_laws : indexed_cat_laws psfunctor_to_indexed_cat_data.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.IndexedCategories.IndexedCategory UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.OppositeCategory.Core UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Discreteness UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Examples.DiscreteBicat UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor