Lemma eq_Cone_eq (a b : Cone) (p q : a = b) : base_paths _ _ (base_paths _ _ p) = base_paths _ _ (base_paths _ _ q) -> p = q. Proof. intro H. assert (H2 : base_paths _ _ p = base_paths _ _ q). apply eq_ConeData_eq. apply H. apply (eq_equalities_between_pairs _ _ _ _ _ _ H2). apply uip. apply isasetaprop. apply isaprop_ConeProp. 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.