Definition ptlz_state_compat {hole_symbs hole_word hole_sems}
  (ptlz:ptl_zipper hole_symbs hole_word hole_sems)
  (state:state): Prop :=
  state_has_future state (ptlz_prod ptlz) hole_symbs
    (projT1 (Streams.hd (ptlz_buffer ptlz))).

(* Specifications: *)
Lemma ptlz_stack_compat_ptlz_state_compat: forall hole_symbs hole_word hole_sems (ptlz:ptl_zipper hole_symbs hole_word hole_sems) (stack:stack), ptlz_stack_compat ptlz stack -> ptlz_state_compat ptlz (state_of_stack init stack).