(* We need to know that the term type checks.  But if it does, our annotated operational semantics corresponds with parallel reduction. *)

(* Specifications: *)
Lemma head_reduction_erased : forall G a b, head_reduction G a b ->
forall A, AnnTyping G a A ->  Par G (dom G) (erase a) (erase b).
Lemma preservation : forall G a A, AnnTyping G a A -> forall a', head_reduction G a a' -> AnnTyping G a' A.
End fc_preservation.