proposition: Lemma eq_ConeData_eq (a b : ConeData) (p q : a = b) : base_paths _ _ p = base_paths _ _ q -> p = q.
proof: Proof. intro H. apply (eq_equalities_between_pairs _ _ _ _ _ _ H). apply uip. apply (impred 2); intro j. apply C. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors