From e978da8c41d8a3c19a29036d9c569fbe2a4616b0 Mon Sep 17 00:00:00 2001
From: Samuel Mimram <smimram@debian.org>
Date: Fri, 16 Jun 2006 14:41:51 +0000
Subject: Imported Upstream version 8.0pl3+8.1beta

---
 test-suite/success/Omega0.v | 149 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 149 insertions(+)
 create mode 100644 test-suite/success/Omega0.v

(limited to 'test-suite/success/Omega0.v')

diff --git a/test-suite/success/Omega0.v b/test-suite/success/Omega0.v
new file mode 100644
index 00000000..4614c90d
--- /dev/null
+++ b/test-suite/success/Omega0.v
@@ -0,0 +1,149 @@
+Require Import ZArith Omega.
+Open Scope Z_scope.
+
+(* Pierre L: examples gathered while debugging romega. *)
+
+Lemma test_romega_0 : 
+ forall m m', 
+  0<= m <= 1 -> 0<= m' <= 1 -> (0 < m <-> 0 < m') -> m = m'.
+Proof.
+intros.
+(*omega.*)
+Admitted.
+
+Lemma test_romega_0b : 
+ forall m m', 
+  0<= m <= 1 -> 0<= m' <= 1 -> (0 < m <-> 0 < m') -> m = m'.
+Proof.
+intros m m'.
+(*omega.*)
+Admitted.
+
+Lemma test_romega_1 : 
+ forall (z z1 z2 : Z), 
+    z2 <= z1 ->
+    z1 <= z2 ->
+    z1 >= 0 ->
+    z2 >= 0 ->
+    z1 >= z2 /\ z = z1 \/ z1 <= z2 /\ z = z2 ->
+    z >= 0.
+Proof.
+intros.
+omega.
+Qed.
+
+Lemma test_romega_1b : 
+ forall (z z1 z2 : Z), 
+    z2 <= z1 ->
+    z1 <= z2 ->
+    z1 >= 0 ->
+    z2 >= 0 ->
+    z1 >= z2 /\ z = z1 \/ z1 <= z2 /\ z = z2 ->
+    z >= 0.
+Proof.
+intros z z1 z2.
+omega.
+Qed.
+
+Lemma test_romega_2 : forall a b c:Z, 
+ 0<=a-b<=1 -> b-c<=2 -> a-c<=3.
+Proof.
+intros.
+omega.
+Qed.
+
+Lemma test_romega_2b : forall a b c:Z, 
+ 0<=a-b<=1 -> b-c<=2 -> a-c<=3.
+Proof.
+intros a b c.
+omega.
+Qed.
+
+Lemma test_romega_3 : forall a b h hl hr ha hb, 
+ 0 <= ha - hl <= 1 -> 
+ -2 <= hl - hr <= 2 ->
+ h =b+1 ->
+ (ha >= hr /\ a = ha \/ ha <= hr /\ a = hr) ->
+ (hl >= hr /\ b = hl \/ hl <= hr /\ b = hr) ->
+ (-3 <= ha -hr <=3 -> 0 <= hb - a <= 1) ->
+ (-2 <= ha-hr <=2 -> hb = a  + 1) -> 
+ 0 <= hb - h <= 1.
+Proof.
+intros.
+omega.
+Qed.
+
+Lemma test_romega_3b : forall a b h hl hr ha hb, 
+ 0 <= ha - hl <= 1 -> 
+ -2 <= hl - hr <= 2 ->
+ h =b+1 ->
+ (ha >= hr /\ a = ha \/ ha <= hr /\ a = hr) ->
+ (hl >= hr /\ b = hl \/ hl <= hr /\ b = hr) ->
+ (-3 <= ha -hr <=3 -> 0 <= hb - a <= 1) ->
+ (-2 <= ha-hr <=2 -> hb = a  + 1) -> 
+ 0 <= hb - h <= 1.
+Proof.
+intros a b h hl hr ha hb.
+omega.
+Qed.
+
+
+Lemma test_romega_4 : forall hr ha, 
+ ha = 0 ->
+ (ha = 0 -> hr =0) -> 
+ hr = 0.
+Proof.
+intros hr ha.
+omega.
+Qed.
+
+Lemma test_romega_5 : forall hr ha, 
+ ha = 0 ->
+ (~ha = 0 \/ hr =0) -> 
+ hr = 0.
+Proof.
+intros hr ha.
+omega.
+Qed.
+
+Lemma test_romega_6 : forall z, z>=0 -> 0>z+2 -> False.
+Proof.
+intros.
+omega.
+Qed.
+
+Lemma test_romega_6b : forall z, z>=0 -> 0>z+2 -> False.
+Proof.
+intros z.
+omega.
+Qed.
+
+Lemma test_romega_7 : forall z, 
+  0>=0 /\ z=0 \/ 0<=0 /\ z =0 -> 1 = z+1.
+Proof.
+intros.
+omega.
+Qed.
+
+Lemma test_romega_7b : forall z, 
+  0>=0 /\ z=0 \/ 0<=0 /\ z =0 -> 1 = z+1.
+Proof.
+intros.
+omega.
+Qed.
+
+(* Magaud #240 *)
+
+Lemma test_romega_8 : forall x y:Z, x*x<y*y-> ~ y*y <= x*x.
+intros.
+omega.
+Qed.
+
+Lemma test_romega_8b : forall x y:Z, x*x<y*y-> ~ y*y <= x*x.
+intros x y.
+omega.
+Qed.
+
+
+
+
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