proposition: Lemma Qpos_sum_eq_join_meet@{} : forall a b c d : Q+, a + b = c + d -> a + b = join a c + meet b d.
proof: Proof. intros ???? E. apply pos_eq;apply Q_sum_eq_join_meet. change (' a + ' b) with (' (a + b)). rewrite E;reflexivity. 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