From 6b649aba925b6f7462da07599fe67ebb12a3460e Mon Sep 17 00:00:00 2001
From: Samuel Mimram <samuel.mimram@ens-lyon.org>
Date: Wed, 28 Jul 2004 21:54:47 +0000
Subject: Imported Upstream version 8.0pl1

---
 test-suite/success/Case12.v | 60 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 60 insertions(+)
 create mode 100644 test-suite/success/Case12.v

(limited to 'test-suite/success/Case12.v')

diff --git a/test-suite/success/Case12.v b/test-suite/success/Case12.v
new file mode 100644
index 00000000..284695f4
--- /dev/null
+++ b/test-suite/success/Case12.v
@@ -0,0 +1,60 @@
+(* This example was proposed by Cuihtlauac ALVARADO *)
+
+Require PolyList.
+
+Fixpoint mult2 [n:nat] : nat :=
+Cases n of
+| O => O
+| (S n) => (S (S (mult2 n)))
+end.
+
+Inductive list : nat -> Set :=
+| nil : (list O)
+| cons : (n:nat)(list (mult2 n))->(list (S (S (mult2 n)))).
+
+Type
+[P:((n:nat)(list n)->Prop);
+ f:(P O nil);
+ f0:((n:nat; l:(list (mult2 n)))
+      (P (mult2 n) l)->(P (S (S (mult2 n))) (cons n l)))]
+ Fix F
+   {F [n:nat; l:(list n)] : (P n l) :=
+      <P>Cases l of
+        nil => f
+      | (cons n0 l0) => (f0 n0 l0 (F (mult2 n0) l0))
+      end}.
+
+Inductive list' : nat -> Set :=
+| nil' : (list' O)
+| cons' : (n:nat)[m:=(mult2 n)](list' m)->(list' (S (S m))).
+
+Fixpoint length [n; l:(list' n)] : nat :=
+  Cases l of
+     nil' => O
+  | (cons' _ m l0) => (S (length m l0))
+  end.
+
+Type
+[P:((n:nat)(list' n)->Prop);
+ f:(P O nil');
+ f0:((n:nat)
+      [m:=(mult2 n)](l:(list' m))(P m l)->(P (S (S m)) (cons' n l)))]
+ Fix F
+   {F [n:nat; l:(list' n)] : (P n l) :=
+      <P>
+        Cases l of
+          nil' => f
+        | (cons' n0 m l0) => (f0 n0 l0 (F m l0))
+        end}.
+
+(* Check on-the-fly insertion of let-in patterns for compatibility *)
+
+Inductive list'' : nat -> Set :=
+| nil'' : (list'' O)
+| cons'' : (n:nat)[m:=(mult2 n)](list'' m)->[p:=(S (S m))](list'' p).
+
+Check Fix length { length [n; l:(list'' n)] : nat :=
+         Cases l of
+           nil'' => O
+         | (cons'' n l0) => (S (length (mult2 n) l0))
+         end }.
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