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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
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Local Open Scope R_scope.
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(*              R is complete :                     *)
(*        Each sequence which satisfies             *)
(*       the Cauchy's criterion converges           *)
(*                                                  *)
(*    Proof with adjacent sequences (Vn and Wn)     *)
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Theorem R_complete :
forall Un:nat -> R, Cauchy_crit Un -> { l:R | Un_cv Un l } .