
theorem
  for M be non empty MetrSpace,
      S be non empty Subset of M holds
      S is sequentially_compact
    iff
      (M|S) is compact
  proof
    let M be non empty MetrSpace,
        S be non empty Subset of M;
    (M|S) is sequentially_compact iff (M|S) is compact by Th11;
    hence thesis by Th14;
  end;
