reserve Y for TopStruct;
reserve X for non empty TopSpace;

theorem
  for A, B being Subset of X st A is open & B is open holds A is
  discrete & B is discrete implies A \/ B is discrete
proof
  let A, B be Subset of X;
  assume that
A1: A is open and
A2: B is open;
  assume that
A3: A is discrete and
A4: B is discrete;
  for P, Q being Subset of X st P is open & Q is open holds P /\ Q is open
  & P \/ Q is open;
  hence thesis by A1,A2,A3,A4,Th24;
end;
