theorem
  for i be Nat
  holds 0.diff_SP(i+1,E,F) = [#]E --> 0.diff_SP(i,E,F)
  proof
    let i be Nat;
    diff_SP(i+1,E,F)
     = R_NormSpace_of_BoundedLinearOperators(E,(diff_SP(i,E,F))) by NDIFF_6:10;
    hence thesis by LOPBAN_1:31;
  end;
