proposition: Lemma Qpos_lt_min@{} : forall a b : Q+, exists c ca cb : Q+, a = c + ca /\ b = c + cb.
proof: Proof. intros. destruct (total le (' a) (' b)) as [E|E]. - apply Qpos_le_lt_min;trivial. - apply Qpos_le_lt_min in E. destruct E as [c [cb [ca [E1 E2]]]]. exists c,ca,cb;auto. 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