Lemma is_precategory_Cone : is_precategory Cone_precategory_data. Proof. repeat split; simpl. intros; apply Cone_Mor_eq; simpl; apply id_left. intros; apply Cone_Mor_eq; simpl; apply id_right. intros; apply Cone_Mor_eq; simpl; apply assoc. intros; apply Cone_Mor_eq; simpl; apply assoc'. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors.