proposition: Lemma Qabs_nonpos_0@{} : forall q : Q, abs q <= 0 -> q = 0.
proof: Proof. intros q E. pose proof (antisymmetry le _ _ E (Qabs_nonneg _)) as E1. destruct (total_abs_either q) as [[E2 E3]|[E2 E3]];rewrite E3 in E1. - trivial. - apply (injective (-)). rewrite negate_0. 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