theorem
  (cdif(f,h).1)/.x = Shift(f,((2*1.F)"*h))/.x - Shift(f,-((2*1.F)"*h))/.x
proof
  set f2 = Shift(f,-((2*1.F)"*h));
  set f1 = Shift(f,((2*1.F)"*h));
  (cdif(f,h).1)/.x = cdif(f,h).(0+1)/.x
  .= cD(cdif(f,h).0,h)/.x by Def8
  .= cD(f,h)/.x by Def8
  .= f/.(x+(2*1.F)"*h) - f/.(x-(2*1.F)"*h) by Th5
  .= f1/.x - f/.(x+-((2*1.F)"*h)) by Def2
  .= f1/.x - f2/.x by Def2;
  hence thesis;
end;
