From a0cfa4f118023d35b767a999d5a2ac4b082857b4 Mon Sep 17 00:00:00 2001
From: Samuel Mimram <smimram@debian.org>
Date: Fri, 25 Jul 2008 15:12:53 +0200
Subject: Imported Upstream version 8.2~beta3+dfsg

---
 test-suite/success/OmegaPre.v | 127 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 127 insertions(+)
 create mode 100644 test-suite/success/OmegaPre.v

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

diff --git a/test-suite/success/OmegaPre.v b/test-suite/success/OmegaPre.v
new file mode 100644
index 00000000..bb800b7a
--- /dev/null
+++ b/test-suite/success/OmegaPre.v
@@ -0,0 +1,127 @@
+Require Import ZArith Nnat Omega.
+Open Scope Z_scope.
+
+(** Test of the zify preprocessor for (R)Omega *)
+
+(* More details in file PreOmega.v
+ 
+   (r)omega with Z        : starts with zify_op
+   (r)omega with nat      : starts with zify_nat
+   (r)omega with positive : starts with zify_positive
+   (r)omega with N        : starts with uses zify_N
+   (r)omega with *        : starts zify (a saturation of the others)
+*)
+
+(* zify_op *)
+
+Goal forall a:Z, Zmax a a = a.
+intros.
+omega with *.
+Qed.
+
+Goal forall a b:Z, Zmax a b = Zmax b a.
+intros.
+omega with *.
+Qed.
+
+Goal forall a b c:Z, Zmax a (Zmax b c) = Zmax (Zmax a b) c.
+intros.
+omega with *.
+Qed.
+
+Goal forall a b:Z, Zmax a b + Zmin a b = a + b.
+intros.
+omega with *.
+Qed.
+
+Goal forall a:Z, (Zabs a)*(Zsgn a) = a.
+intros.
+zify.
+intuition; subst; omega. (* pure multiplication: omega alone can't do it *)
+Qed.
+
+Goal forall a:Z, Zabs a = a -> a >= 0.
+intros.
+omega with *.
+Qed.
+
+Goal forall a:Z, Zsgn a = a -> a = 1 \/ a = 0 \/ a = -1.
+intros.
+omega with *.
+Qed.
+
+(* zify_nat *)
+
+Goal forall m: nat, (m<2)%nat -> (0<= m+m <=2)%nat.
+intros.
+omega with *.
+Qed.
+
+Goal forall m:nat, (m<1)%nat -> (m=0)%nat.
+intros.
+omega with *.
+Qed.
+
+Goal forall m: nat, (m<=100)%nat -> (0<= m+m <=200)%nat.
+intros.
+omega with *.
+Qed.
+(* 2000 instead of 200: works, but quite slow *)
+
+Goal forall m: nat, (m*m>=0)%nat.
+intros.
+omega with *.
+Qed.
+
+(* zify_positive *)
+
+Goal forall m: positive, (m<2)%positive -> (2 <= m+m /\ m+m <= 2)%positive.
+intros.
+omega with *.
+Qed.
+
+Goal forall m:positive, (m<2)%positive -> (m=1)%positive.
+intros.
+omega with *.
+Qed.
+
+Goal forall m: positive, (m<=1000)%positive -> (2<=m+m/\m+m <=2000)%positive.
+intros.
+omega with *.
+Qed.
+
+Goal forall m: positive, (m*m>=1)%positive.
+intros.
+omega with *.
+Qed.
+
+(* zify_N *)
+
+Goal forall m:N, (m<2)%N -> (0 <= m+m /\ m+m <= 2)%N.
+intros.
+omega with *.
+Qed.
+
+Goal forall m:N, (m<1)%N -> (m=0)%N.
+intros.
+omega with *.
+Qed.
+
+Goal forall m:N, (m<=1000)%N -> (0<=m+m/\m+m <=2000)%N.
+intros.
+omega with *.
+Qed.
+
+Goal forall m:N, (m*m>=0)%N.
+intros.
+omega with *.
+Qed.
+
+(* mix of datatypes *)
+
+Goal forall p, Z_of_N (N_of_nat (nat_of_N (Npos p))) = Zpos p.
+intros.
+omega with *.
+Qed.
+
+
-- 
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