Lemma Par_lc1 : forall G D a a' , Par G D a a' -> lc_tm a.
  intros.  induction H; auto. all: lc_solve.
Qed.

(* FIXME: find a good place for this tactic. *)
(* cannot move this to ett_ind.v because need Toplevel_lc ??? *)
Ltac lc_toplevel_inversion :=
  ma

Lemma Par_respects_atoms: forall G D a b, Par G D a b -> forall D', D [=] D' -> Par G D' a b.