(**************************************************************************)
(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
(**************************************************************************)

(* This file was automatically generated: do not edit *********************)

include "Coq.ma".

(*#***********************************************************************)

(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)

(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)

(*   \VV/  **************************************************************)

(*    //   *      This file is distributed under the terms of the       *)

(*         *       GNU Lesser General Public License Version 2.1        *)

(*#***********************************************************************)

(* $Id: Zsqrt.v,v 1.11.2.1 2004/07/16 19:31:22 herbelin Exp $ *)

include "ZArith/ZArith_base.ma".

(* UNEXPORTED
Open Local Scope Z_scope.
*)

(*#*********************************************************************)

(*#* Definition and properties of square root on Z *)

(*#* The following tactic replaces all instances of (POS (xI ...)) by
    `2*(POS ...)+1`, but only when ... is not made only with xO, XI, or xH. *)

(* UNEXPORTED
Ltac compute_POS :=
  match goal with
  |  |- context [(Zpos (xI ?X1))] =>
      match constr:X1 with
      | context [1%positive] => fail
      | _ => rewrite (BinInt.Zpos_xI X1)
      end
  |  |- context [(Zpos (xO ?X1))] =>
      match constr:X1 with
      | context [1%positive] => fail
      | _ => rewrite (BinInt.Zpos_xO X1)
      end
  end.
*)

inline procedural "cic:/Coq/ZArith/Zsqrt/sqrt_data.ind".

inline procedural "cic:/Coq/ZArith/Zsqrt/sqrtrempos.con" as definition.

(*#* Define with integer input, but with a strong (readable) specification. *)

inline procedural "cic:/Coq/ZArith/Zsqrt/Zsqrt.con" as definition.

(*#* Define a function of type Z->Z that computes the integer square root,
    but only for positive numbers, and 0 for others. *)

inline procedural "cic:/Coq/ZArith/Zsqrt/Zsqrt_plain.con" as definition.

(*#* A basic theorem about Zsqrt_plain *)

inline procedural "cic:/Coq/ZArith/Zsqrt/Zsqrt_interval.con" as theorem.