reserve r for Real;
reserve a, b for Real;
reserve T for non empty TopSpace;
reserve A for non empty SubSpace of T;
reserve P,Q for Subset of T,
  p for Point of T;
reserve M for non empty MetrSpace,
  p for Point of M;
reserve A for non empty SubSpace of M;
reserve F,G for Subset-Family of M;

theorem
  for T being non empty TopSpace, A,B being Subset of T st A c= B holds
  T|A is SubSpace of T|B
proof
  let T be non empty TopSpace, A,B be Subset of T;
  assume A c= B;
  then A \/ B = B by XBOOLE_1:12;
  hence thesis by Th4;
end;
