Decomposition de Cases

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@1651 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 36 insertions, 0 deletions

diff --git a/test-suite/success/Case8.v b/test-suite/success/Case8.v
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+Inductive empty : (n:nat)(listn n)-> Prop := 
+  intro_empty: (empty O niln).
+
+Parameter inv_empty : (n,a:nat)(l:(listn n)) ~(empty (S n) (consn n a l)).
+
+Type 
+[n:nat] [l:(listn n)]
+  <[n:nat] [l:(listn n)](empty n l) \/ ~(empty n l)>Cases l of 
+        niln               =>  (or_introl ? ~(empty O niln) intro_empty)
+   |  ((consn n O y) as b) =>  (or_intror (empty (S n) b) ? (inv_empty n O y))
+   |  ((consn n a y) as b) =>  (or_intror (empty (S n) b) ? (inv_empty n a y))
+
+  end.
+
+
+Type 
+[n:nat] [l:(listn n)]
+  <[n:nat] [l:(listn n)](empty n l) \/ ~(empty n l)>Cases l of 
+        niln               =>  (or_introl ? ~(empty O niln) intro_empty)
+   |  (consn n O y)  =>  (or_intror (empty (S n) (consn n O y)) ? 
+                                              (inv_empty n O y))
+   |  (consn n a y) =>  (or_intror (empty (S n) (consn n a y)) ? 
+                                          (inv_empty n a y))
+
+  end.
+
+
+
+Type 
+[n:nat] [l:(listn n)]
+  <[n:nat] [l:(listn n)](empty n l) \/ ~(empty n l)>Cases l of 
+        niln               =>  (or_introl ? ~(empty O niln) intro_empty)
+   |  ((consn O a y) as b) =>  (or_intror (empty (S O) b) ? (inv_empty O a y))
+   |  ((consn n a y) as b) =>  (or_intror (empty (S n) b) ? (inv_empty n a y))
+
+  end.