Lemma eq_CONE_pr1 (M N : CONE F) (p q : M = N) : base_paths _ _ p = base_paths _ _ q -> p = q. Proof. intro H. simpl in *. apply (eq_equalities_between_pairs _ _ _ _ _ _ H). apply proofirrelevancecontr. 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.