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 Th12:
  [!(f1+f2),x0,x1,x2,x3,x4!] = [!f1,x0,x1,x2,x3,x4!]+[!f2,x0,x1,x2 ,x3,x4!]
proof
  [!(f1+f2),x0,x1,x2,x3,x4!] = ([!f1,x0,x1,x2,x3!]+[!f2,x0,x1,x2,x3!] - [!
  (f1+f2),x1,x2,x3,x4!])/(x0-x4) by Th9
    .= ([!f1,x0,x1,x2,x3!]+[!f2,x0,x1,x2,x3!] - ([!f1,x1,x2,x3,x4!]+[!f2,x1,
  x2,x3,x4!]))/(x0-x4) by Th9
    .= (([!f1,x0,x1,x2,x3!] - [!f1,x1,x2,x3,x4!]) + ([!f2,x0,x1,x2,x3!] - [!
  f2,x1,x2,x3,x4!]))/(x0-x4);
  hence thesis by XCMPLX_1:62;
end;
