Definition binproductleft_map_laws: psfunctor_laws binproductleft_map_data. Proof. repeat split; red; cbn. - intros A A' F. apply (nat_trans_eq (homset_property (productwithfixedelement _))). intro ab. cbn. apply idpath. - intros A A' F1 F2 F3 α β. apply (nat_trans_eq (homset_property (productwithfixedelement _))). intro ab. cbn. apply pathsdirprod. * apply idpath. * apply pathsinv0, id_left. - intros A B F. apply (nat_trans_eq (homset_property (productwithfixedelement _))). intro ab. cbn. apply pathsdirprod. * do 2 rewrite id_right. apply pathsinv0, functor_id. * do 2 rewrite id_right. apply idpath. - intros A B F. apply (nat_trans_eq (homset_property (productwithfixedelement _))). intro ab. cbn. apply pathsdirprod; do 2 rewrite id_right; apply idpath. - intros A1 A2 A3 A4 F G H. apply (nat_trans_eq (homset_property (productwithfixedelement _))). intro a1b. cbn. apply pathsdirprod. * do 3 rewrite id_left. rewrite id_right. apply pathsinv0, functor_id. * apply idpath. - intros A1 A2 A3 F G1 G2 β. apply (nat_trans_eq (homset_property (productwithfixedelement _))). intro a1b. cbn. apply pathsdirprod. * rewrite id_left, id_right. apply idpath. * apply idpath. - intros A1 A2 A3 F1 F2 G α. apply (nat_trans_eq (homset_property (productwithfixedelement _))). intro a1b. cbn. apply pathsdirprod. * rewrite id_left, id_right. apply idpath. * apply idpath. Defined.
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.