theorem
  for S,T be RealNormSpace holds RLSStruct (# ContinuousFunctions(S,T),
    Zero_(ContinuousFunctions(S,T),RealVectSpace(the carrier of S,T)),
    Add_(ContinuousFunctions(S,T),RealVectSpace(the carrier of S,T)),
    Mult_(ContinuousFunctions(S,T), RealVectSpace(the carrier of S,T))
      #) is Subspace of RealVectSpace(the carrier of S,T)
        by Th11,RSSPACE:11;
