reserve i for Integer,
  a, b, r, s for Real;

theorem
  for X, Y being TopSpace, Z being open SubSpace of Y, f being Function
  of X, Y, g being Function of X, Z st f = g & g is open holds f is open
proof
  let X, Y be TopSpace, Z be open SubSpace of Y, f be Function of X, Y, g be
  Function of X, Z such that
A1: f = g and
A2: g is open;
  let A be Subset of X;
  assume A is open;
  then g.:A is open by A2;
  hence thesis by A1,TSEP_1:17;
end;
