proposition: Lemma Qlowbound_lt_ZExp2_spec : forall (q : Q) (Hqgt0 : q > 0), (2^(Qlowbound_ltabs_ZExp2 q) < q)%Q.
proof: Proof. intros q Hqgt0. pose proof Qbound_ltabs_ZExp2_spec (/q) as Hspecub. rewrite Qlowbound_ltabs_ZExp2_inv by exact Hqgt0. rewrite Qpower_opp. setoid_rewrite <- (Qinv_involutive q) at 2. apply -> Qinv_lt_contravar. - rewrite Qabs_pos in Hspecub. + exact Hspecub. + apply Qlt_le_weak, Qinv_lt_0_compat, Hqgt0. - apply Qpower_0_lt; lra. - apply Qinv_lt_0_compat, Hqgt0. Qed.
imports: QArith Qpower Qabs Qround Lia Lqa PosExtra