reserve m, n, i, k for Nat;
reserve IAlph, OAlph for non empty set,
  fsm for non empty FSM over IAlph,
  s for Element of IAlph,
  w, w1, w2 for FinSequence of IAlph,
  q, q9, q1, q2 for State of fsm;

theorem
  ((q, w)-admissible).(len (q, w)-admissible) = q9 iff q, w -leads_to q9
by Def2;
