Local Ltac simplify_Qabs :=
  match goal with |- context [(Qabs ?a)%Q] => ring_simplify a end.Local Ltac simplify_Qlt :=
  match goal with |- (?l < ?r)%Q => ring_simplify l; ring_simplify r end.

Local Lemma Qabs_involutive: forall q : Q, (Qabs (Qabs q) == Qabs q)%Q.