theorem
  for A being non empty automaton over Lex(E) \/ {<%>E} ex DA being non
  empty deterministic automaton over Lex(E) st Lang(A) = Lang(DA)
proof
  let A be non empty automaton over Lex(E) \/ {<%>E};
  set DA = _bool A;
  take DA;
  thus thesis by Th38;
end;
