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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)           *)
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(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
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Local Open Scope R_scope.
(* Proving a few formulas in the style of John Machin to compute Pi *)
Definition atan_sub u v := (u - v)/(1 + u * v).

(* A simple formula, reasonably efficient. *)
Lemma Machin_2_3 : PI/4 = atan(/2) + atan(/3).