reserve A, B for non empty set,
  A1, A2, A3 for non empty Subset of A;

theorem
  for f1 being Function of A1,B, f2 being Function of A2,B st
  f1|(A1 /\ A2) = f2|(A1 /\ A2) holds f1 union f2 = f2 union f1
proof
  let f1 be Function of A1,B, f2 be Function of A2,B;
  assume f1|(A1 /\ A2) = f2|(A1 /\ A2);
  then (f1 union f2)|A1 = f1 & (f1 union f2)|A2 = f2 by Def1;
  hence thesis by Th2;
end;
