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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].
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