Module Import Valid := Validator_safe.Make A.Proposition shift_head_symbs: shift_head_symbs.Proposition goto_head_symbs: goto_head_symbs.Proposition shift_past_state: shift_past_state.Proposition goto_past_state: goto_past_state.Proposition reduce_ok: reduce_ok.(** The stack of symbols of an automaton stack **)
Definition symb_stack_of_stack (stack:stack) :=
  List.map
    (fun cell:sigT noninitstate_type => last_symb_of_non_init_state (projT1 cell))
    stack.

Lemma prefix_pred_ass: forall (l1 l2 l3:list (state->bool)), prefix_pred l1 l2 -> prefix_pred l2 l3 -> prefix_pred l1 l3.