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(* as published by the Free Software Foundation; either version 2.1   *)
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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
(* Large approximation of PI *)
Definition PI_lb : R := 3%R.
Definition PI_ub : R := 4%R.

(* Specifications: *)
(* 3 < PI < 4 *)
Lemma PI_approx : (PI_lb < PI < PI_ub)%R.
Proof with trivial.