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-rw-r--r--theories/Numbers/Integer/Abstract/ZBase.v8
-rw-r--r--theories/Numbers/Integer/Abstract/ZDomain.v4
-rw-r--r--theories/Numbers/Integer/Abstract/ZMulOrder.v6
3 files changed, 9 insertions, 9 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZBase.v b/theories/Numbers/Integer/Abstract/ZBase.v
index 29e18548..0f71f2cc 100644
--- a/theories/Numbers/Integer/Abstract/ZBase.v
+++ b/theories/Numbers/Integer/Abstract/ZBase.v
@@ -8,7 +8,7 @@
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
-(*i $Id: ZBase.v 11040 2008-06-03 00:04:16Z letouzey $ i*)
+(*i $Id: ZBase.v 11674 2008-12-12 19:48:40Z letouzey $ i*)
Require Export Decidable.
Require Export ZAxioms.
@@ -36,14 +36,14 @@ Proof NZpred_succ.
Theorem Zeq_refl : forall n : Z, n == n.
Proof (proj1 NZeq_equiv).
-Theorem Zeq_symm : forall n m : Z, n == m -> m == n.
+Theorem Zeq_sym : forall n m : Z, n == m -> m == n.
Proof (proj2 (proj2 NZeq_equiv)).
Theorem Zeq_trans : forall n m p : Z, n == m -> m == p -> n == p.
Proof (proj1 (proj2 NZeq_equiv)).
-Theorem Zneq_symm : forall n m : Z, n ~= m -> m ~= n.
-Proof NZneq_symm.
+Theorem Zneq_sym : forall n m : Z, n ~= m -> m ~= n.
+Proof NZneq_sym.
Theorem Zsucc_inj : forall n1 n2 : Z, S n1 == S n2 -> n1 == n2.
Proof NZsucc_inj.
diff --git a/theories/Numbers/Integer/Abstract/ZDomain.v b/theories/Numbers/Integer/Abstract/ZDomain.v
index 15beb2b9..9a17e151 100644
--- a/theories/Numbers/Integer/Abstract/ZDomain.v
+++ b/theories/Numbers/Integer/Abstract/ZDomain.v
@@ -8,7 +8,7 @@
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
-(*i $Id: ZDomain.v 10934 2008-05-15 21:58:20Z letouzey $ i*)
+(*i $Id: ZDomain.v 11674 2008-12-12 19:48:40Z letouzey $ i*)
Require Export NumPrelude.
@@ -49,7 +49,7 @@ assert (x == y); [rewrite Exx'; now rewrite Eyy' |
rewrite <- H2; assert (H3 : e x y); [now apply -> eq_equiv_e | now inversion H3]]].
Qed.
-Theorem neq_symm : forall n m, n # m -> m # n.
+Theorem neq_sym : forall n m, n # m -> m # n.
Proof.
intros n m H1 H2; symmetry in H2; false_hyp H2 H1.
Qed.
diff --git a/theories/Numbers/Integer/Abstract/ZMulOrder.v b/theories/Numbers/Integer/Abstract/ZMulOrder.v
index e3f1d9aa..c7996ffd 100644
--- a/theories/Numbers/Integer/Abstract/ZMulOrder.v
+++ b/theories/Numbers/Integer/Abstract/ZMulOrder.v
@@ -8,7 +8,7 @@
(* Evgeny Makarov, INRIA, 2007 *)
(************************************************************************)
-(*i $Id: ZMulOrder.v 11040 2008-06-03 00:04:16Z letouzey $ i*)
+(*i $Id: ZMulOrder.v 11674 2008-12-12 19:48:40Z letouzey $ i*)
Require Export ZAddOrder.
@@ -173,7 +173,7 @@ Notation Zmul_neg := Zlt_mul_0 (only parsing).
Theorem Zle_0_mul :
forall n m : Z, 0 <= n * m -> 0 <= n /\ 0 <= m \/ n <= 0 /\ m <= 0.
Proof.
-assert (R : forall n : Z, 0 == n <-> n == 0) by (intros; split; apply Zeq_symm).
+assert (R : forall n : Z, 0 == n <-> n == 0) by (intros; split; apply Zeq_sym).
intros n m. repeat rewrite Zlt_eq_cases. repeat rewrite R.
rewrite Zlt_0_mul, Zeq_mul_0.
pose proof (Zlt_trichotomy n 0); pose proof (Zlt_trichotomy m 0). tauto.
@@ -184,7 +184,7 @@ Notation Zmul_nonneg := Zle_0_mul (only parsing).
Theorem Zle_mul_0 :
forall n m : Z, n * m <= 0 -> 0 <= n /\ m <= 0 \/ n <= 0 /\ 0 <= m.
Proof.
-assert (R : forall n : Z, 0 == n <-> n == 0) by (intros; split; apply Zeq_symm).
+assert (R : forall n : Z, 0 == n <-> n == 0) by (intros; split; apply Zeq_sym).
intros n m. repeat rewrite Zlt_eq_cases. repeat rewrite R.
rewrite Zlt_mul_0, Zeq_mul_0.
pose proof (Zlt_trichotomy n 0); pose proof (Zlt_trichotomy m 0). tauto.