
theorem PRETOPC18:
  for X be RealNormSpace, Z be Subset of X holds Z c= Cl(Z)
  proof
    let X be RealNormSpace, Z be Subset of X;
    reconsider W = Z as Subset of LinearTopSpaceNorm X by NORMSP_2:def 4;
    Cl Z = Cl W by EQCL1;
    hence Z c= Cl Z by PRE_TOPC:18;
  end;
