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(* $Id$ *)
(* Instantiation of the Ring tactic for the binary integers of ZArith *)
Require Export ArithRing.
Require Export ZArith.
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; Unfold Zeq.
Generalize (let (H1,H2)=(Zcompare_EGAL x y) in H1).
Elim (Zcompare x y); [Intro; Rewrite H; Trivial | 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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