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 Th1:
  (q, <*>IAlph)-admissible = <*q*>
proof
  set eis = <*>IAlph;
A1: for i being Nat st 1 <= i & i <= len eis ex wi being Element of IAlph,
  qi, qi1 being State of fsm st wi=eis.i & qi=<*q*>.i & qi1=<*q*>.(i+1)& wi
  -succ_of qi=qi1;
  len <*q*> = len eis + 1 & <*q*>.1 = q by FINSEQ_1:40;
  hence thesis by A1,Def2;
end;
