proposition: Lemma is_functor_BinProduct_of_functors_data : is_functor BinProduct_of_functors_data.
proof: Proof. split; simpl; intros. - red; intros; simpl in *. apply pathsinv0. unfold BinProduct_of_functors_mor. apply BinProduct_endo_is_identity. + rewrite BinProductOfArrowsPr1. rewrite functor_id. apply id_right. + rewrite BinProductOfArrowsPr2. rewrite functor_id. apply id_right. - red; intros; simpl in *. unfold BinProduct_of_functors_mor. do 2 rewrite functor_comp. apply pathsinv0. apply BinProductOfArrows_comp. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorCategory UniMath.Combinatorics.StandardFiniteSets