(** The identity cone morph. *)
    Program Definition LoKan_id_Cone_Morph : LoKan_Cone_Morph Cn Cn :=
      {|
        cone_morph := NatTrans_id _
      |}.(** Composition of cone morphs. *)
    Program Definition LoKan_Cone_Morph_compose : LoKan_Cone_Morph Cn Cn'' :=
      {|
        cone_morph := NatTrans_compose h h'
      |}.

(* Specifications: *)
Theorem LoKan_Cone_Morph_compose_assoc : LoKan_Cone_Morph_compose h (LoKan_Cone_Morph_compose h' h'') = LoKan_Cone_Morph_compose (LoKan_Cone_Morph_compose h h') h''.
Theorem LoKan_id_Cone_Morph_unit_right : LoKan_Cone_Morph_compose (LoKan_id_Cone_Morph _) h = h.
Theorem LoKan_id_Cone_Morph_unit_left : LoKan_Cone_Morph_compose h (LoKan_id_Cone_Morph _) = h.