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-(************************************************************************)
-(* 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: ZArithRing.v,v 1.1.2.1 2004/07/16 19:30:19 herbelin Exp $ *)
-
-(* Instantiation of the Ring tactic for the binary integers of ZArith *)
-
-Require Export ArithRing.
-Require Export ZArith_base.
-Require Eqdep_dec.
-
-Definition Zeq := [x,y:Z]
- Cases `x ?= y ` of
- EGAL => true
- | _ => false
- end.
-
-Lemma Zeq_prop : (x,y:Z)(Is_true (Zeq x y)) -> x==y.
- Intros x y H; Unfold Zeq in H.
- Apply Zcompare_EGAL_eq.
- NewDestruct (Zcompare x y); [Reflexivity | Contradiction | Contradiction ].
-Save.
-
-Definition ZTheory : (Ring_Theory Zplus Zmult `1` `0` Zopp Zeq).
- Split; Intros; Apply eq2eqT; EAuto with zarith.
- Apply eqT2eq; Apply Zeq_prop; Assumption.
-Save.
-
-(* NatConstants and NatTheory are defined in Ring_theory.v *)
-Add Ring Z Zplus Zmult `1` `0` Zopp Zeq ZTheory [POS NEG ZERO xO xI xH].