theorem
  (bdif(f,h).1)/.x = f/.x - Shift(f,-h)/.x
proof
  set f2 = Shift(f,-h);
  (bdif(f,h).1)/.x = bdif(f,h).(0+1)/.x
  .= bD(bdif(f,h).0,h)/.x by Def7
  .= bD(f,h)/.x by Def7
  .= f/.x - f/.(x-h) by Th4
  .= f/.x - f2/.x by Def2;
  hence thesis;
end;
