(* This version of the proof is incredibly slow. *)
(*
  all: pre; basic_solve.
  all: try oh_c'mon.
  all: try invert_open_wrt.
  all: try pick fresh c for L.
  all: try eapply lc_a_UCAbs_exists; eauto.
  all: try apply H; eauto.
  all: eapply (lc_a_UAbs_exists c). rewrite e. eauto. done.
Qed.*)

Definition Typing_lc  := first lc_mutual.Definition PropWff_lc := second lc_mutual.Definition Iso_lc     := third lc_mutual.Definition DefEq_lc   := fourth lc_mutual.Definition Ctx_lc     := fifth lc_mutual.

Lemma Toplevel_lc : forall c s, binds c s toplevel -> lc_sig_sort s.