proposition: Lemma Qabs_nonneg@{} : forall q : Q, 0 <= abs q.
proof: Proof. intros q;destruct (total_abs_either q) as [E|E];destruct E as [E1 E2];rewrite E2. - trivial. - apply flip_nonneg_negate. rewrite involutive;trivial. 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