proposition: Lemma bifunctor_to_functor_to_bifunctor {C D E : category} (F : bifunctor C D E) : bifunctor_from_functorfromproductcat (bifunctor_to_functorfromproductcat F) = F.
proof: Proof. use total2_paths_f. { apply bifunctor_to_functor_to_bifunctor_data. } apply isaprop_is_bifunctor. 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