proposition: Lemma all_reals_locators (x : F) : locator x.
proof: Proof. intros q r ltqr. case (LEM (' q < x)). - apply _. - exact inl. - intros notlt. apply inr. assert (ltqr' : ' q < ' r) by auto. exact (nlt_lt_trans notlt ltqr'). 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