reserve x,r,a,x0,p for Real;
reserve n,i,m for Element of NAT;
reserve Z for open Subset of REAL;
reserve f,f1,f2 for PartFunc of REAL,REAL;
reserve k for Nat;

theorem
  f is_differentiable_on n,Z implies diff(-f,Z).n = -diff(f,Z).n & -f
  is_differentiable_on n,Z
by Th21,Th22;
