proposition: Lemma curry_functor_data_is_functor: is_functor curry_functor_data.
proof: Proof. split. - intro d. apply (nat_trans_eq E). intro c. cbn. unfold nat_trans_from_functor_fix_snd_morphism_arg_data. etrans. { apply maponpaths. apply binprod_id. } apply functor_id. - intros d1 d2 d3 f g. apply (nat_trans_eq E). intro c. cbn. unfold nat_trans_from_functor_fix_snd_morphism_arg_data. etrans. 2: { apply functor_comp. } apply maponpaths. apply dirprodeq; cbn. + apply pathsinv0. apply id_left. + apply idpath. 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.FunctorCategory UniMath.CategoryTheory.opp_precat