proposition: Lemma is_precategory_product_precategory_data : is_precategory product_precategory_data.
proof: Proof. repeat split; intros; apply funextsec; intro i. - apply id_left. - apply id_right. - apply assoc. - apply assoc'. Defined.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.opp_precat