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diff --git a/plugins/nsatz/NsatzZ.v b/plugins/nsatz/NsatzZ.v
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-(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
-(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(************************************************************************)
-
-Require Import Reals ZArith.
-Require Export NsatzR.
-
-Open Scope Z_scope.
-
-Lemma nsatzZhypR: forall x y:Z, x=y -> IZR x = IZR y.
-Proof IZR_eq. (* or f_equal ... *)
-
-Lemma nsatzZconclR: forall x y:Z, IZR x = IZR y -> x = y.
-Proof eq_IZR.
-
-Lemma nsatzZhypnotR: forall x y:Z, x<>y -> IZR x <> IZR y.
-Proof IZR_neq.
-
-Lemma nsatzZconclnotR: forall x y:Z, IZR x <> IZR y -> x <> y.
-Proof.
-intros x y H. contradict H. f_equal. assumption.
-Qed.
-
-Ltac nsatzZtoR1 :=
- repeat
- (match goal with
- | H:(@eq Z ?x ?y) |- _ =>
- generalize (@nsatzZhypR _ _ H); clear H; intro H
- | |- (@eq Z ?x ?y) => apply nsatzZconclR
- | H:not (@eq Z ?x ?y) |- _ =>
- generalize (@nsatzZhypnotR _ _ H); clear H; intro H
- | |- not (@eq Z ?x ?y) => apply nsatzZconclnotR
- end).
-
-Lemma nsatzZR1: forall x y:Z, IZR(x+y) = (IZR x + IZR y)%R.
-Proof plus_IZR.
-
-Lemma nsatzZR2: forall x y:Z, IZR(x*y) = (IZR x * IZR y)%R.
-Proof mult_IZR.
-
-Lemma nsatzZR3: forall x y:Z, IZR(x-y) = (IZR x - IZR y)%R.
-Proof.
-intros; symmetry. apply Z_R_minus.
-Qed.
-
-Lemma nsatzZR4: forall (x:Z) p, IZR(x ^ Zpos p) = (IZR x ^ nat_of_P p)%R.
-Proof.
-intros. rewrite pow_IZR.
-do 2 f_equal.
-apply Zpos_eq_Z_of_nat_o_nat_of_P.
-Qed.
-
-Ltac nsatzZtoR2:=
- repeat
- (rewrite nsatzZR1 in * ||
- rewrite nsatzZR2 in * ||
- rewrite nsatzZR3 in * ||
- rewrite nsatzZR4 in *).
-
-Ltac nsatzZ_begin :=
- intros;
- nsatzZtoR1;
- nsatzZtoR2;
- simpl in *.
- (*cbv beta iota zeta delta [nat_of_P Pmult_nat plus mult] in *.*)
-
-Ltac nsatzZ :=
- nsatzZ_begin; (*idtac "nsatzZ_begin;";*)
- nsatzR.