theorem
  fdif(f1+r(#)f2,h).(n+1).x = fdif(f1,h).(n+1).x + r* fdif(f2,h).(n+1).x
proof
  set g=r(#)f2;
  fdif(f1+r(#)f2,h).(n+1).x = fdif(f1,h).(n+1).x + fdif(g,h).(n+1).x
                                                          by DIFF_1:8
    .= fdif(f1,h).(n+1).x + r* fdif(f2,h).(n+1).x by DIFF_1:7;
  hence thesis;
end;
