theorem
  for FA being non empty finite automaton over Lex(E) \/ {<%>E} ex DFA
being non empty deterministic finite automaton over Lex(E) st Lang(FA) = Lang(
  DFA)
proof
  let FA be non empty finite automaton over Lex(E) \/ {<%>E};
  set bNFA = _bool FA;
  Lang(FA) = Lang(bNFA) by Th38;
  hence thesis;
end;
