reserve x, y, X for set;
reserve E for non empty set;
reserve e for Element of E;
reserve u, u1, v, v1, v2, w, w9, w1, w2 for Element of E^omega;
reserve F for Subset of E^omega;
reserve i, k, l for Nat;
reserve TS for non empty transition-system over F;
reserve S, T for Subset of TS;
reserve SA for non empty semiautomaton over F;
reserve A for non empty automaton over F;
reserve p, q for Element of A;
reserve TS for non empty transition-system over Lex(E) \/ {<%>E};
reserve SA for non empty semiautomaton over Lex(E) \/ {<%>E};
reserve A for non empty automaton over Lex(E) \/ {<%>E};
reserve P for Subset of A;

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;
