reserve S,T for RealNormSpace;
reserve f,f1,f2 for PartFunc of S,T;
reserve Z for Subset of S;
reserve i,n for Nat;

theorem Th10:
for i be Nat holds
  diff_SP(i+1,S,T) = R_NormSpace_of_BoundedLinearOperators(S,diff_SP(i,S,T))
proof
   let i be Nat;
   set H = diff_SP(i,S,T);
   ex H1 be RealNormSpace st H1 = (diff_SP(S,T)).i
  & (diff_SP(S,T)).(i+1) = R_NormSpace_of_BoundedLinearOperators(S,H1)
      by Th9;
   hence thesis;
end;
