(** ** Power of 2 open lower bounds for [2^z < q] and [2^z < Qabs q] *)
(** Note: the -2 is required cause of the Qlt limit. In case q is a power of two, the lower and upper bound must be a factor of 4 apart *)
Definition Qlowbound_ltabs_ZExp2 (q : Q) : Z := -2 + Qbound_ltabs_ZExp2 q.

Lemma Qlowbound_ltabs_ZExp2_inv: forall q : Q,
q > 0
-> Qlowbound_ltabs_ZExp2 q = (- Qbound_ltabs_ZExp2 (/q))%Z.