End interchangelaw.
(* o_NTh is associative *)
Definition EqualH_NT (C D : Category) (F G F' G' : Functor C D)
(T : NT F G) (T' : NT F' G') := forall a : C, T a =_H T' a.
Infix "=_NTH" := EqualH_NT (at level 70).
Section assoc_horz_comp.
Variables (A B C D : Category) (F G : Functor A B)
(F' G' : Functor B C) (F'' G'' : Functor C D).
Variables (T : NT F G) (T' : NT F' G') (T'' : NT F'' G'').

(* Specifications: *)
Lemma CompH_NT_assoc : (T o_NTh T') o_NTh T'' =_NTH T o_NTh T' o_NTh T''.
End assoc_horz_comp.