Section nt_def.
Variables (C D : Category) (F G : Functor C D).
Definition NT_law (T : forall a : C, F a --> G a) :=
forall (a b : C) (f : a --> b), FMor F f o T b =_S T a o FMor G f.
Structure > NT : Type :=
{ApNT :> forall a : C, F a --> G a; Prf_NT_law :> NT_law ApNT}.
(*** rewrite rules ***)

Lemma NatCond1 :
forall (T : NT) (a b : C) (f : a --> b), T a o FMor G f =_S FMor F f o T b.