
theorem Th11:
  for M be non empty MetrSpace holds
    TopSpaceMetr M is compact iff M is sequentially_compact
  proof
    let M be non empty MetrSpace;
    thus TopSpaceMetr M is compact implies M is sequentially_compact
      by Th8,COMPL_SP:35;
    assume M is sequentially_compact; then
    M is totally_bounded complete by Th10;
    hence TopSpaceMetr M is compact by COMPL_SP:37;
  end;
