reserve x,y for Real,
  i, j for non zero Element of NAT,
  I, O for non empty set,
  s,s1,s2,s3 for Element of I,
  w, w1, w2 for FinSequence of I,
  t for Element of O,
  S for non empty FSM over I,
  q, q1 for State of S;
reserve n, m, o, p for non zero Element of NAT,
  M for non empty Moore-SM_Final over I, O,
  q for State of M;

theorem
  the InitS of M in the FinalS of M implies
  (the OFun of M).the InitS of M is_result_of s, M
proof
  assume
A1: the InitS of M in the FinalS of M;
  take 1;
  let w;
  assume w.1 = s;
  thus thesis by A1,FSM_1:def 2,NAT_1:14;
end;
