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
  [!sin(#)sin,x0,x1!] = (1/2)*(cos(2*x1)-cos(2*x0))/(x0-x1)
proof
  [!sin(#)sin,x0,x1!] = ((sin.x0)*(sin.x0)-(sin(#)sin).x1) /(x0-x1) by
VALUED_1:5
    .= (sin(x0)*sin(x0)-sin(x1)*sin(x1))/(x0-x1) by VALUED_1:5
    .= (-(1/2)*(cos(x0+x0)-cos(x0-x0)) -sin(x1)*sin(x1))/(x0-x1) by SIN_COS4:29
    .= (-(1/2)*(cos(x0+x0)-cos(x0-x0))- -(1/2)*(cos(x1+x1)-cos(x1-x1)))/(x0-
  x1) by SIN_COS4:29
    .= (1/2)*(cos(2*x1)-cos(2*x0))/(x0-x1);
  hence thesis;
end;
