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

Lemma FixDef_FixTy : AnnTyping nil FixDef FixTy.