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 Th8:
  [!(r(#)f),x0,x1,x2,x3!] = r*[!f,x0,x1,x2,x3!]
proof
  [!(r(#)f),x0,x1,x2,x3!] = (r*[!f,x0,x1,x2!]-[!(r(#)f),x1,x2,x3!]) /(x0-
  x3) by Th5
    .= (r*[!f,x0,x1,x2!]-r*[!f,x1,x2,x3!])/(x0-x3) by Th5
    .= (r*([!f,x0,x1,x2!]-[!f,x1,x2,x3!]))/(x0-x3);
  hence thesis by XCMPLX_1:74;
end;
