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