
theorem Th18:
  for X be RealNormSpace, Y be Subset of X holds
    the carrier of NLin(Y) c= the carrier of ClNLin(Y)
  & ex Z be Subset of X
    st Z = the carrier of NLin(Y) & Cl(Z) = the carrier of ClNLin(Y)
  proof
    let X be RealNormSpace, Y be Subset of X;
    ex Z be Subset of X
    st Z = the carrier of Lin(Y)
     & ClNLin(Y) = NORMSTR(# Cl(Z), Zero_(Cl(Z),X), Add_(Cl(Z),X),
               Mult_(Cl(Z),X), Norm_(Cl(Z),X) #) by NORMSP_3:def 20;
    hence thesis by NORMSP_3:4;
end;
