proposition: Lemma Q_triangle_le : forall q r : Q, abs (q + r) <= abs q + abs r.
proof: Proof. intros. rewrite (Qabs_is_join (q + r)). apply join_le. - rewrite negate_plus_distr. apply plus_le_compat;apply Qabs_le_neg_raw. - apply plus_le_compat;apply Qabs_le_raw. 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