From 3dcd1844ac8d5554093afc254ed8ee5c294546e3 Mon Sep 17 00:00:00 2001
From: herbelin
Date: Wed, 2 Jun 2004 15:50:10 +0000
Subject: Nouveaux thms de non circularité de nat

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@5795 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Arith/Plus.v | 27 ++++++++++++++++++++++++++-
 1 file changed, 26 insertions(+), 1 deletion(-)

diff --git a/theories/Arith/Plus.v b/theories/Arith/Plus.v
index 496ac33303..7ed40b6c34 100755
--- a/theories/Arith/Plus.v
+++ b/theories/Arith/Plus.v
@@ -199,4 +199,29 @@ Definition tail_plus n m := plus_acc m n.
 Lemma plus_tail_plus : forall n m, n + m = tail_plus n m.
 unfold tail_plus in |- *; induction n as [| n IHn]; simpl in |- *; auto.
 intro m; rewrite <- IHn; simpl in |- *; auto.
-Qed.
\ No newline at end of file
+Qed.
+
+(** Discrimination *)
+
+Lemma succ_plus_discr : forall n m, n <> S (plus m n).
+Proof.
+intros n m; induction n as [|n IHn].
+ discriminate.
+ intro H; apply IHn; apply eq_add_S; rewrite H; rewrite <- plus_n_Sm; 
+   reflexivity.
+Qed.
+
+Lemma n_SSn : forall n, n <> S (S n).
+Proof.
+intro n; exact (succ_plus_discr n 1).
+Qed.
+
+Lemma n_SSSn : forall n, n <> S (S (S n)).
+Proof.
+intro n; exact (succ_plus_discr n 2).
+Qed.
+
+Lemma n_SSSSn : forall n, n <> S (S (S (S n))).
+Proof.
+intro n; exact (succ_plus_discr n 3).
+Qed.
-- 
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