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 Th6:
  [!(f1+f2),x0,x1,x2!] = [!f1,x0,x1,x2!]+[!f2,x0,x1,x2!]
proof
  [!(f1+f2),x0,x1,x2!] = ([!f1,x0,x1!]+[!f2,x0,x1!]-[!(f1+f2),x1,x2!])/(x0
  -x2) by DIFF_1:32
    .= ([!f1,x0,x1!]+[!f2,x0,x1!] -([!f1,x1,x2!]+[!f2,x1,x2!]))/(x0-x2) by
DIFF_1:32
    .= (([!f1,x0,x1!]-[!f1,x1,x2!]) +([!f2,x0,x1!]-[!f2,x1,x2!]))/(x0-x2);
  hence thesis by XCMPLX_1:62;
end;
