theorem Th18:
  f1 is_differentiable_on n,Z & f2 is_differentiable_on n,Z & i<=n
  implies diff(f1-f2,Z).i = diff(f1,Z).i - diff(f2,Z).i
proof
  assume
A1: f1 is_differentiable_on n,Z & f2 is_differentiable_on n,Z;
  assume i<=n;
  then f1 is_differentiable_on i, Z & f2 is_differentiable_on i, Z by A1,
TAYLOR_1:23;
  hence thesis by Th16;
end;
