 reserve RNS1,RNS2 for RealLinearSpace;

theorem
  for RNS be RealNormSpace
   st RNS is finite-dimensional
     holds ex T be NormedLinearTopSpace
           st the NORMSTR of RNS = the NORMSTR of T & T is finite-dimensional
proof
let RNS be RealNormSpace;
assume A1: RNS is finite-dimensional;
consider T be NormedLinearTopSpace such that
A2: the NORMSTR of RNS = the NORMSTR of T by Th23;
take T;
the RLSStruct of T = the RLSStruct of RNS by A2;
hence thesis by Th21, A1, A2;
end;
