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 Th5:
  [!(r(#)f),x0,x1,x2!] = r*[!f,x0,x1,x2!]
proof
  [!(r(#)f),x0,x1,x2!] = (r*[!f,x0,x1!]-[!(r(#)f),x1,x2!]) /(x0-x2) by
DIFF_1:31
    .= (r*[!f,x0,x1!]-r*[!f,x1,x2!])/(x0-x2) by DIFF_1:31
    .= (r*([!f,x0,x1!]-[!f,x1,x2!]))/(x0-x2);
  hence thesis by XCMPLX_1:74;
end;
