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 Th9:
  [!(f1+f2),x0,x1,x2,x3!]=[!f1,x0,x1,x2,x3!]+[!f2,x0,x1,x2,x3!]
proof
  [!(f1+f2),x0,x1,x2,x3!] = ([!f1,x0,x1,x2!]+[!f2,x0,x1,x2!] - [!(f1+f2),
  x1,x2,x3!])/(x0-x3) by Th6
    .= ([!f1,x0,x1,x2!]+[!f2,x0,x1,x2!] - ([!f1,x1,x2,x3!]+[!f2,x1,x2,x3!]))
  /(x0-x3) by Th6
    .= (([!f1,x0,x1,x2!] - [!f1,x1,x2,x3!]) + ([!f2,x0,x1,x2!] - [!f2,x1,x2,
  x3!]))/(x0-x3);
  hence thesis by XCMPLX_1:62;
end;
