reserve E, F, G,S,T,W,Y for RealNormSpace;
reserve f,f1,f2 for PartFunc of S,T;
reserve Z for Subset of S;
reserve i,n for Nat;

theorem Th56:
  for S,E,F be RealNormSpace,
      i be Nat
  holds
  CTP(S,diff_SP(i,S,E),diff_SP(i,S,F)) is Lipschitzian LinearOperator of
    [:diff_SP(i+1,S,E),diff_SP(i+1,S,F):],
    R_NormSpace_of_BoundedLinearOperators(S,[:diff_SP(i,S,E),diff_SP(i,S,F):])
proof
  let S,E,F be RealNormSpace,
      i be Nat;

  set E1 = diff_SP(i,S,E);
  set F1 = diff_SP(i,S,F);

  A1: R_NormSpace_of_BoundedLinearOperators(S,E1)
    = diff_SP(i+1,S,E) by NDIFF_6:10;

  R_NormSpace_of_BoundedLinearOperators(S,F1)
    = diff_SP(i+1,S,F) by NDIFF_6:10;
  hence thesis by A1;
end;
