proposition: Lemma pos_recip_through_plus@{} : forall a b c : Q+, a + b = c * (a / c + b / c).
proof: Proof. intros. path_via ((a + b) * (c / c)). - rewrite pos_recip_r;apply pos_eq,symmetry,mult_1_r. - apply pos_eq;ring_tac.ring_with_nat. 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