theorem
  f1 is_differentiable_in x0 & f2 is_differentiable_in x0 implies
  f1-f2 is_differentiable_in x0 & diff(f1-f2,x0) = diff(f1,x0)-diff(f2,x0)
proof
A1: f1-f2 = f1+-f2 by Th1;
    assume
A2: f1 is_differentiable_in x0;
    assume f2 is_differentiable_in x0;
    then -f2 is_differentiable_in x0 & diff(-f2,x0) = -diff(f2,x0) by Th10;
    hence thesis by A1,A2,Th11;
end;
