Lemma eq_ConeData_eq (a b : ConeData) (p q : a = b) : base_paths _ _ p = base_paths _ _ q -> p = q. Proof. intro H. apply (eq_equalities_between_pairs _ _ _ _ _ _ H). apply uip. apply (impred 2); intro j. apply C. 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.