proposition: Lemma bifunctor_to_functor_to_bifunctor_data {C D E : category} (F : bifunctor C D E) : pr1 (bifunctor_from_functorfromproductcat (bifunctor_to_functorfromproductcat F)) = pr1 F.
proof: Proof. repeat (use total2_paths_f). - apply idpath. - repeat (apply funextsec ; intro). apply when_bifunctor_becomes_leftwhiskering. - repeat (apply funextsec ; intro). etrans. { rewrite transportf_const. apply when_bifunctor_becomes_rightwhiskering. } apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.ProductCategory