(* 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. *)

Lemma reduction_preservation : forall a a', reduction_in_one a a' -> forall G A, Typing G a A -> Typing G a' A.
Ltac par_with_context_tail :=
match goal with
| _ : _ |- Par ([?s] ++ ?G ) (dom ([?s] ++ ?G)) ?a ?b =>
eapply context_Par_irrelevance with (G1 := G) (D1 := dom G); eauto
end.