
theorem
  for X be RealBanachSpace, M be non empty Subset of X
  st M is linearly-closed & M is closed
  holds NLin(M) is RealBanachSpace
  proof
    let X be RealBanachSpace, M be non empty Subset of X;
    assume
    A1: M is linearly-closed & M is closed; then
    the carrier of NLin(M) = M by LCL1;
    hence thesis by A1,LM76A;
  end;
