proposition: Lemma locator_join : locator (join x y).
proof: Proof. intros q r ltqr. destruct (l q r ltqr, m q r ltqr) as [[ltqx|ltxr] [ltqy|ltyr]]. - apply inl, join_lt_l_l; assumption. - apply inl, join_lt_l_l; assumption. - apply inl, join_lt_l_r; assumption. - apply inr, join_lt_r; assumption. Qed.
imports: HoTT.Basics HoTT.DProp HoTT.BoundedSearch HoTT.Spaces.Finite.Fin HoTT.ExcludedMiddle HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.interfaces.rationals HoTT.Classes.interfaces.cauchy HoTT.Classes.interfaces.archimedean HoTT.Classes.interfaces.round HoTT.Classes.interfaces.naturals HoTT.Classes.implementations.peano_naturals HoTT.Classes.orders.archimedean HoTT.Classes.orders.dec_fields HoTT.Classes.orders.lattices HoTT.Classes.theory.apartness HoTT.Classes.theory.rationals HoTT.Classes.orders.fields HoTT.Classes.theory.fields HoTT.Classes.theory.dec_fields