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+Inductive listn : nat-> Set :=
+ niln : (listn O)
+| consn : (n:nat)nat->(listn n) -> (listn (S n)).
+
+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.