proposition: Lemma Qabs_triangle_alt : forall x y : Q, abs (abs x - abs y) <= abs (x - y).
proof: Proof. intros q r. rewrite (Qabs_is_join (abs q - abs r)). apply join_le. - rewrite <-(Qabs_neg (q - r)),<-!negate_swap_r. apply Qabs_triangle_alt_aux. - apply Qabs_triangle_alt_aux. 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