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