reserve h,r,r1,r2,x0,x1,x2,x3,x4,x5,x,a,b,c,k for Real,
  f,f1,f2 for Function of REAL,REAL;

theorem
  for x holds cD(cos,h).x = -2*(sin(x)*sin(h/2))
proof
  let x;
  cD(cos,h).x = cos(x+h/2)-cos(x-h/2) by DIFF_1:5
    .= -2*(sin((x+h/2+(x-h/2))/2) *sin((x+h/2-(x-h/2))/2)) by SIN_COS4:18;
  hence thesis;
end;
