theorem
  bdif(f1+r(#)f2,h).(n+1).x = bdif(f1,h).(n+1).x + r* bdif(f2,h).(n+1).x
proof
  set g=r(#)f2;
  bdif(f1+r(#)f2,h).(n+1).x = bdif(f1,h).(n+1).x + bdif(g,h).(n+1).x
                                                           by DIFF_1:15
    .= bdif(f1,h).(n+1).x + r* bdif(f2,h).(n+1).x by DIFF_1:14;
  hence thesis;
end;
