`{Funext} C D HO HM HC HI : ap object (@path_precategory_uncurried' _ C D (HO; (HM; (HC, HI)))) = HO. Proof. destruct C, D; cbn in *. path_induction_hammer. Qed.
Require Import Category.Core. Require Import HoTT.Basics.Equivalences HoTT.Basics.PathGroupoids HoTT.Basics.Trunc HoTT.Basics.Tactics. Require Import HoTT.Types.Sigma HoTT.Types.Arrow HoTT.Types.Forall. Require Import HoTT.Tactics.