
theorem
  for X be RealBanachSpace, Y be Subset of X st X is Reflexive
  holds ClNLin(Y) is Reflexive
  proof
    let X be RealBanachSpace, Y be Subset of X;
    assume A1: X is Reflexive;
    ex Z be Subset of X
    st Z = the carrier of Lin(Y) & ClNLin(Y) = NLin(Cl(Z))
     & Cl(Z) is linearly-closed & Cl(Z) <> {} by Th35;
    hence thesis by A1,DUALSP02:24;
  end;
