(* ---------------------------------------------------------- *)

Ltac use_binder f x :=
  pick fresh x and apply f;
  unfold open_tm_wrt_tm; simpl; simpl_env; eauto;
  match goal with
    [ |- Typing ?ctx ?a ?A ] =>
    assert (Ctx ctx); [econstructor; eauto|idtac]
  end.

Lemma FixDef_FixTy_erase : Typing nil (erase_tm FixDef) (erase_tm FixTy).