reserve X for TopStruct,
  A for Subset of X;
reserve X for TopSpace,
  A,B for Subset of X;

theorem Th5:
  for A being Subset of X st A is closed holds Int(A \/ B) c= A \/ Int B
proof
  let A be Subset of X;
  assume A is closed;
  then Cl A = A by PRE_TOPC:22;
  hence thesis by Th4;
end;
