 reserve RNS1,RNS2 for RealLinearSpace;

theorem  Th25:
  for T be NormedLinearTopSpace,
    RNS be RealNormSpace
  st T is finite-dimensional & RNS = the NORMSTR of T
holds
  RNS is finite-dimensional & dim RNS = dim T
proof
let T be NormedLinearTopSpace,
  RNS be RealNormSpace;
assume A1: T is finite-dimensional
         & RNS = the NORMSTR of T; then
the RLSStruct of T = the RLSStruct of RNS;
hence thesis by Th21, A1;
end;
