proposition: Lemma pos_split2@{} : forall e : Q+, e = e / 2 + e / 2.
proof: Proof. intros. path_via (e * (2 / 2)). - rewrite pos_recip_r,pos_mult_1_r;reflexivity. - apply pos_eq. change (' e * (2 / 2) = ' e / 2 + ' e / 2). 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