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 bD(sin,h).x = 2*(cos((2*x-h)/2)*sin(h/2))
proof
  let x;
  bD(sin,h).x = sin(x)-sin(x-h) by DIFF_1:4
    .= 2*(cos((x+(x-h))/2)*sin((x-(x-h))/2)) by SIN_COS4:16;
  hence thesis;
end;
