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-rw-r--r--theories/ZArith/Wf_Z.v8
-rw-r--r--theories/ZArith/Zmisc.v20
-rw-r--r--theories/ZArith/fast_integer.v2
-rw-r--r--theories/ZArith/zarith_aux.v2
4 files changed, 16 insertions, 16 deletions
diff --git a/theories/ZArith/Wf_Z.v b/theories/ZArith/Wf_Z.v
index 27c760194..65571855e 100644
--- a/theories/ZArith/Wf_Z.v
+++ b/theories/ZArith/Wf_Z.v
@@ -35,11 +35,11 @@ Require Zsyntax.
Lemma inject_nat_complete :
(x:Z)`0 <= x` -> (EX n:nat | x=(inject_nat n)).
-Destruct x; Intros;
+NewDestruct x; Intros;
[ Exists O; Auto with arith
| Specialize (ZL4 p); Intros Hp; Elim Hp; Intros;
- Exists (S x0); Intros; Simpl;
- Specialize (bij1 x0); Intro Hx0;
+ Exists (S x); Intros; Simpl;
+ Specialize (bij1 x); Intro Hx0;
Rewrite <- H0 in Hx0;
Apply f_equal with f:=POS;
Apply convert_intro; Auto with arith
@@ -61,7 +61,7 @@ Save.
Lemma inject_nat_complete_inf :
(x:Z)`0 <= x` -> { n:nat | (x=(inject_nat n)) }.
-Destruct x; Intros;
+NewDestruct x; Intros;
[ Exists O; Auto with arith
| Specialize (ZL4_inf p); Intros Hp; Elim Hp; Intros x0 H0;
Exists (S x0); Intros; Simpl;
diff --git a/theories/ZArith/Zmisc.v b/theories/ZArith/Zmisc.v
index dc9e69e17..cf46b8bdf 100644
--- a/theories/ZArith/Zmisc.v
+++ b/theories/ZArith/Zmisc.v
@@ -261,12 +261,12 @@ Save.
Lemma Zeven_not_Zodd : (z:Z)(Zeven z) -> ~(Zodd z).
Proof.
- Destruct z; [ Idtac | Destruct p | Destruct p ]; Compute; Trivial.
+ NewDestruct z; [ Idtac | NewDestruct p | NewDestruct p ]; Compute; Trivial.
Save.
Lemma Zodd_not_Zeven : (z:Z)(Zodd z) -> ~(Zeven z).
Proof.
- Destruct z; [ Idtac | Destruct p | Destruct p ]; Compute; Trivial.
+ NewDestruct z; [ Idtac | NewDestruct p | NewDestruct p ]; Compute; Trivial.
Save.
Hints Unfold Zeven Zodd : zarith.
@@ -291,22 +291,22 @@ Definition Zdiv2 :=
Lemma Zeven_div2 : (x:Z) (Zeven x) -> `x = 2*(Zdiv2 x)`.
Proof.
-Destruct x.
+NewDestruct x.
Auto with arith.
-Destruct p; Auto with arith.
-Intros. Absurd (Zeven (POS (xI p0))); Red; Auto with arith.
+NewDestruct p; Auto with arith.
+Intros. Absurd (Zeven (POS (xI p))); Red; Auto with arith.
Intros. Absurd (Zeven `1`); Red; Auto with arith.
-Destruct p; Auto with arith.
-Intros. Absurd (Zeven (NEG (xI p0))); Red; Auto with arith.
+NewDestruct p; Auto with arith.
+Intros. Absurd (Zeven (NEG (xI p))); Red; Auto with arith.
Intros. Absurd (Zeven `-1`); Red; Auto with arith.
Save.
Lemma Zodd_div2 : (x:Z) `x >= 0` -> (Zodd x) -> `x = 2*(Zdiv2 x)+1`.
Proof.
-Destruct x.
+NewDestruct x.
Intros. Absurd (Zodd `0`); Red; Auto with arith.
-Destruct p; Auto with arith.
-Intros. Absurd (Zodd (POS (xO p0))); Red; Auto with arith.
+NewDestruct p; Auto with arith.
+Intros. Absurd (Zodd (POS (xO p))); Red; Auto with arith.
Intros. Absurd `(NEG p) >= 0`; Red; Auto with arith.
Save.
diff --git a/theories/ZArith/fast_integer.v b/theories/ZArith/fast_integer.v
index f64093034..678e8b472 100644
--- a/theories/ZArith/fast_integer.v
+++ b/theories/ZArith/fast_integer.v
@@ -1147,7 +1147,7 @@ Save.
Theorem Zmult_Zopp_Zopp:
(x,y:Z) (Zmult (Zopp x) (Zopp y)) = (Zmult x y).
Proof.
-Destruct x; Destruct y; Reflexivity.
+NewDestruct x; NewDestruct y; Reflexivity.
Save.
Theorem weak_Zmult_plus_distr_r:
diff --git a/theories/ZArith/zarith_aux.v b/theories/ZArith/zarith_aux.v
index 72b66c494..7eb1e37c2 100644
--- a/theories/ZArith/zarith_aux.v
+++ b/theories/ZArith/zarith_aux.v
@@ -46,7 +46,7 @@ Definition Zabs [z:Z] : Z :=
(*s Properties of absolu function *)
Lemma Zabs_eq : (x:Z) (Zle ZERO x) -> (Zabs x)=x.
-Destruct x; Auto with arith.
+NewDestruct x; Auto with arith.
Compute; Intros; Absurd SUPERIEUR=SUPERIEUR; Trivial with arith.
Save.