proposition: Lemma Q_abs_plus_1_bounds@{} : forall q : Q, - ' (pos_of_Q q) ≤ q ≤ ' (pos_of_Q q).
proof: 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.
imports: HoTT.Classes.implementations.peano_naturals HoTT.Classes.implementations.natpair_integers HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.naturals HoTT.Classes.interfaces.rationals HoTT.Classes.interfaces.orders HoTT.Classes.theory.groups HoTT.Classes.theory.integers HoTT.Classes.theory.dec_fields HoTT.Classes.orders.sum HoTT.Classes.orders.dec_fields HoTT.Classes.orders.lattices HoTT.Classes.theory.additional_operations HoTT.Classes.tactics.ring_quote HoTT.Classes.tactics.ring_tac