 reserve S, T for RealNormSpace;
 reserve F for Subset of Funcs(the carrier of S,the carrier of T);
 reserve S,Z for RealNormSpace;
 reserve T for RealBanachSpace;
 reserve F for Subset of Funcs(the carrier of S,the carrier of T);

theorem ThLast:
  for T be NormedLinearTopSpace
    st T is compact holds
      T is complete
proof
  let T be NormedLinearTopSpace;
  assume T is compact; then
  TopSpaceNorm T is compact by Th20; then
  MetricSpaceNorm T is sequentially_compact by TOPMETR4:11;
  hence T is complete by Th6,TOPMETR4:12;
end;
