(* Lemma Par_fv_preservation: forall G D x a b, Par G D a b -> x `notin` fv_tm_tm_tm a -> x `notin` fv_tm_tm_tm b. *)

(* See: reduction_in_one_lc in ext_red_one.  Lemma reduction_lc : forall a a', reduction_in_one a a' -> lc_tm a -> lc_tm a'. *)
Lemma reduction_in_one_fv_preservation: forall x a b, reduction_in_one a b ->
x `notin` fv_tm_tm_tm a ->
x `notin` fv_tm_tm_tm b.