Q_abs_plus_1_bounds@{} : forall q : Q, - ' (pos_of_Q q) ≤ q ≤ ' (pos_of_Q q). Proof. intros. change (- (abs q + 1) ≤ q ≤ (abs q + 1)). split. - apply flip_le_negate. rewrite involutive. transitivity (abs q). + apply Qabs_le_neg_raw. + apply nonneg_plus_le_compat_r. solve_propholds. - transitivity (abs q). + apply Qabs_le_raw. + apply nonneg_plus_le_compat_r. solve_propholds. Qed.
Require Import Import Quoting.Instances. Import NatPair.Instances.