End horz_comp.
Infix "o_NTh" := CompH_NT (at level 20, right associativity).
Section interchangelaw.
Variables (A B C : Category) (F G H : Functor A B) (F' G' H' : Functor B C).
Variables (T : NT F G) (T' : NT F' G') (U : NT G H) (U' : NT G' H').

Lemma InterChange_law :
(T o_NTh T') o_NTv U o_NTh U' =_NT (T o_NTv U) o_NTh T' o_NTv U'.