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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@1996 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 0 insertions, 1596 deletions

diff --git a/test-suite/success/Cases.v b/test-suite/success/Cases.v
deleted file mode 100644
index 313f8f74a..000000000
--- a/test-suite/success/Cases.v
+++ /dev/null
@@ -1,1596 +0,0 @@
-(***********************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team    *)
-(* <O___,, *        INRIA-Rocquencourt  &  LRI-CNRS-Orsay              *)
-(*   \VV/  *************************************************************)
-(*    //   *      This file is distributed under the terms of the      *)
-(*         *       GNU Lesser General Public License Version 2.1       *)
-(***********************************************************************)
-(****************************************************************************)
-(* Pattern-matching when non inductive terms occur                          *)
-
-(* Dependent form of annotation *)
-Type <[n:nat]nat>Cases O eq of O x => O | (S x) y => x end.
-Type <[_,_:nat]nat>Cases O eq O of O x y => O | (S x) y z => x end.
-
-(* Non dependent form of annotation *)
-Type <nat>Cases O eq of O x => O | (S x) y => x end.
-
-(****************************************************************************)
-(* All remaining examples come from Cristina Cornes' V6 TESTS/MultCases.v   *)
-
-Inductive IFExpr : Set := 
-          Var  : nat -> IFExpr
-        | Tr   : IFExpr
-        | Fa   : IFExpr
-        | IfE   : IFExpr -> IFExpr -> IFExpr -> IFExpr.
-
-Inductive List [A:Set] :Set := 
- Nil:(List A) | Cons:A->(List A)->(List A).
-
-Inductive listn : nat-> Set := 
-  niln : (listn O) 
-| consn : (n:nat)nat->(listn n) -> (listn (S n)).
-
-Inductive Listn [A:Set] : nat-> Set := 
-  Niln : (Listn A O) 
-| Consn : (n:nat)nat->(Listn A n) -> (Listn A (S n)).
-
-Inductive Le : nat->nat->Set :=
-  LeO: (n:nat)(Le O n) 
-| LeS: (n,m:nat)(Le n m) -> (Le (S n) (S m)).
-
-Inductive LE [n:nat] : nat->Set := 
-    LE_n : (LE n n) | LE_S : (m:nat)(LE n m)->(LE n (S m)).
-
-Require Bool.
-
-
-
-Inductive PropForm : Set := 
-          Fvar : nat -> PropForm
-        | Or   : PropForm -> PropForm -> PropForm .
-
-Section testIFExpr.
-Definition  Assign:= nat->bool.
-Parameter Prop_sem : Assign -> PropForm -> bool.
-
-Type [A:Assign][F:PropForm] 
-    <bool>Cases F of
-           (Fvar n)   => (A n)
-         | (Or F G)   => (orb (Prop_sem A F) (Prop_sem A G))
-    end.
-
-Type [A:Assign][H:PropForm] 
-    <bool>Cases H of
-           (Fvar n)   => (A n)
-         | (Or F G)   => (orb (Prop_sem A F) (Prop_sem A G))
-    end.
-End testIFExpr.
-
-
-
-Type [x:nat]<nat>Cases x of O => O | x => x end.
-
-Section testlist.
-Parameter A:Set.
-Inductive list : Set := nil : list | cons : A->list->list.
-Parameter inf: A->A->Prop.
-
-
-Definition list_Lowert2 :=
-   [a:A][l:list](<Prop>Cases l of nil => True 
-                               | (cons b l) =>(inf a b) end).
-
-Definition titi :=
-   [a:A][l:list](<list>Cases l of nil => l
-                               | (cons b l) => l end).
-Reset list.
-End testlist.
-
-
-(* To test translation *)
-(* ------------------- *)
-
-
-Type  <nat>Cases O of O => O | _ => O end.
-
-Type <nat>Cases O of
-               (O as b) => b 
-             | (S O)  => O
-             | (S (S x)) => x end.
-
-Type Cases O of
-               (O as b) => b 
-             | (S O)  => O
-             | (S (S x)) => x end.
-
-
-Type [x:nat]<nat>Cases x of
-                          (O as b) => b 
-                        | (S x)  => x end.
-
-Type              [x:nat]Cases x of
-                          (O as b) => b 
-                        | (S x)  => x end.
-
-Type <nat>Cases O of 
-                          (O as b) => b 
-                        | (S x)  => x end.
-
-Type <nat>Cases O of 
-                          x  => x 
-                       end.
-
-Type  Cases O of 
-                          x  => x 
-                       end.
-
-Type <nat>Cases O of
-                              O => O
-                         | ((S x) as b) => b
-                        end.
-
-Type [x:nat]<nat>Cases x of
-                              O => O
-                         | ((S x) as b) => b
-                        end.
-
-Type [x:nat] Cases x of
-                              O => O
-                         | ((S x) as b) => b
-                        end.
-
-
-Type <nat>Cases O of
-         O => O
-    | (S x) => O
-      end.
-
-
-Type <nat*nat>Cases O of
-                              O => (O,O)
-                         | (S x) =>  (x,O)
-                        end.
-
-Type                    Cases O of
-                              O => (O,O)
-                         | (S x) =>  (x,O)
-                        end.
-
-Type <nat->nat>Cases O of
-                              O => [n:nat]O
-                         | (S x) =>  [n:nat]O
-                        end.
-
-Type                   Cases O of
-                              O => [n:nat]O
-                         | (S x) =>  [n:nat]O
-                        end.
-
-
-Type <nat->nat>Cases O of
-                              O => [n:nat]O
-                         | (S x) =>  [n:nat](plus x n)
-                        end.
-
-Type                    Cases O of
-                              O => [n:nat]O
-                         | (S x) =>  [n:nat](plus x n)
-                        end.
-
-
-Type <nat>Cases O of
-                              O => O
-                         | ((S x) as b) => (plus b x)
-                         end.
-
-Type <nat>Cases O of
-              O => O
-          | ((S (x as a)) as b) => (plus b a)
-                         end.
-Type  Cases O of
-              O => O
-          | ((S (x as a)) as b) => (plus b a)
-                         end.
-
-
-Type  Cases O of
-                              O => O
-                         |  _  => O
-                        end.
-
-Type <nat>Cases O of
-                  O => O
-               |  x => x
-                 end.
-
-Type <nat>Cases O (S O) of
-                             x  y => (plus x y)
-                        end.
-
-Type      Cases O (S O) of
-                             x  y => (plus x y)
-                        end.
- 
-Type <nat>Cases O (S O) of
-                             O  y => y
-                          | (S x) y => (plus x y) 
-                        end.
-
-Type              Cases O (S O) of
-                             O  y => y
-                          | (S x) y => (plus x y) 
-                        end.
-
-
-Type    <nat>Cases O (S O) of
-                      O  x =>  x
-             |      (S y) O =>  y
-             |        x y  => (plus x y)
-           end.
-
-
-
-
-Type        Cases O (S O) of
-                      O  x => (plus x O)
-             |      (S y) O =>  (plus y O)
-             |        x y  => (plus x y)
-           end.
-
-Type 
-          <nat>Cases O (S O) of
-                      O  x => (plus x O)
-             |      (S y) O =>  (plus y O)
-             |        x y  => (plus x y)
-           end.
-
-
-Type 
-          <nat>Cases O (S O) of
-                      O  x =>  x 
-             | ((S x) as b) (S y) => (plus (plus b x) y)
-             |    x y  => (plus x y)
-           end.
-
-
-Type         Cases O (S O) of
-                    O  x =>  x 
-             | ((S x) as b) (S y) => (plus (plus b x) y)
-             |    x y  => (plus x y)
-           end.
-
-
-Type [l:(List nat)]<(List nat)>Cases l of 
-                         Nil => (Nil nat)
-                      | (Cons  a l) => l
-                      end.
-
-Type [l:(List nat)]  Cases l of 
-                         Nil => (Nil nat)
-                      | (Cons  a l) => l
-                      end.
-
-Type <nat>Cases (Nil nat) of 
-                         Nil =>O
-                      | (Cons  a l) => (S a)
-                      end.
-Type Cases (Nil nat) of 
-                         Nil =>O
-                      | (Cons  a l) => (S a)
-                      end.
-
-Type <(List nat)>Cases (Nil nat) of 
-                        (Cons  a l) => l
-                       | x => x
-                      end.
-
-Type              Cases (Nil nat) of 
-                        (Cons  a l) => l
-                       | x => x
-                      end.
-
-Type <(List nat)>Cases (Nil nat) of 
-                         Nil => (Nil nat)
-                      | (Cons  a l) => l
-                      end.
-
-Type             Cases (Nil nat) of 
-                         Nil => (Nil nat)
-                      | (Cons  a l) => l
-                      end.
-
-
-Type 
-   <nat>Cases O of 
-      O => O
-    | (S x) => <nat>Cases (Nil nat) of 
-                         Nil => x
-                      | (Cons  a l) => (plus x a)
-                      end
-     end.
-
-Type 
-   Cases O of 
-      O => O
-    | (S x) => Cases (Nil nat) of 
-                         Nil => x
-                      | (Cons  a l) => (plus x a)
-                      end
-     end.
-
-Type 
- [y:nat]Cases y of 
-      O => O
-    | (S x) => Cases (Nil nat) of 
-                         Nil => x
-                      | (Cons  a l) => (plus x a)
-                      end
-     end.
-
-
-Type 
-   <nat>Cases O (Nil nat) of 
-      O       x => O
-    | (S x)  Nil => x
-    | (S x) (Cons  a l) => (plus x a)      
-     end.
-
-
-
-Type [n:nat][l:(listn n)]<[_:nat]nat>Cases l of 
-                         niln => O
-                      |    x  => O
-                      end.
-
-Type [n:nat][l:(listn n)]
-                     Cases l of 
-                         niln => O
-                      |    x  => O
-                      end.
-
-
-Type <[_:nat]nat>Cases niln of 
-                         niln => O
-                      |    x  => O
-                      end.
-
-Type               Cases niln of 
-                         niln => O
-                      |    x  => O
-                      end.
-
-
-Type <[_:nat]nat>Cases niln of 
-                         niln => O
-                      |  (consn n a l)  => a
-                      end.
-Type Cases niln of niln => O
-               |  (consn n a l)  => a
-     end.
-
-
-Type  <[n:nat][_:(listn n)]nat>Cases niln of 
-                         (consn m _ niln) => m
-                       | _ => (S O) end.
-
-
-
-Type [n:nat][x:nat][l:(listn n)]<[_:nat]nat>Cases x l of 
-                         O niln => O
-                      |  y  x  => O
-                      end.
-
-Type <[_:nat]nat>Cases O niln of 
-                         O niln => O
-                      |  y  x  => O
-                      end.
-
-
-Type <[_:nat]nat>Cases niln O of 
-                         niln O => O
-                      |  y  x  => O
-                      end.
-
-Type               Cases niln O of 
-                         niln O => O
-                      |  y  x  => O
-                      end.
-
-Type <[_:nat][_:nat]nat>Cases niln niln of 
-                         niln niln => O
-                      |    x  y  => O
-                      end.
-
-Type               Cases niln niln of 
-                         niln niln => O
-                      |    x  y  => O
-                      end.
-
-Type <[_,_,_:nat]nat>Cases niln niln niln of 
-                         niln niln niln => O
-                      |    x  y z  => O
-                      end.
-
-
-Type                 Cases niln niln niln of 
-                         niln niln niln => O
-                      |    x  y z  => O
-                      end.
-
-
-
-Type <[_:nat]nat>Cases (niln) of 
-                         niln  => O
-                      | (consn n a l) => O
-                      end.
-
-Type         Cases (niln) of 
-                         niln  => O
-                      | (consn n a l) => O
-                      end.
-
-
-Type <[_:nat][_:nat]nat>Cases niln niln of 
-                         niln niln => O
-                      |  niln (consn n a l) => n
-                      |  (consn n a l)  x  => a
-                      end.
-
-
-Type                Cases niln niln of 
-                         niln niln => O
-                      |  niln (consn n a l) => n
-                      |  (consn n a l)  x  => a
-                      end.
-
-
-Type [n:nat][l:(listn n)]<[_:nat]nat>Cases l of 
-                         niln => O
-                      |    x  => O
-                      end.
-
-Type [c:nat;s:bool]
-  <[_:nat;_:bool]nat>Cases c s of
-        | O _ => O
-        | _ _ => c
-        end.
-
-Type [c:nat;s:bool]
-  <[_:nat;_:bool]nat>Cases c s of
-        | O _ => O
-        | (S _) _ => c
-        end.
-         
-
-(* Rows of pattern variables: some tricky cases *)
-Axiom P:nat->Prop; f:(n:nat)(P n).
-
-Type [i:nat]
-  <[_:bool;n:nat](P n)>Cases true i of
-        | true k => (f k)
-        | _    k => (f k)
-        end.
-
-Type [i:nat]
-  <[n:nat;_:bool](P n)>Cases i true of
-        | k true => (f k)
-        | k _ => (f k)
-        end.
-
-(* Nested Cases: the SYNTH of the Cases on n used to make Multcase believe
- * it has to synthtize the predicate on O (which he can't)
- *)
-Type <[n]Cases n of O => bool | (S _) => nat end>Cases O of
-    O => true
-  | (S _) => O
-  end.
-
-Type [n:nat][l:(listn n)]Cases l of 
-                         niln => O
-                      |    x  => O
-                      end.
-
-Type [n:nat][l:(listn n)]<[_:nat]nat>Cases l of 
-                         niln  => O
-                      | (consn n a niln) => O
-                      | (consn n a (consn m b l)) => (plus n m)
-                      end.
-
-
-Type [n:nat][l:(listn n)]Cases l of 
-                         niln  => O
-                      | (consn n a niln) => O
-                      | (consn n a (consn m b l)) => (plus n m)
-                      end.
-
-
-
-Type [n:nat][l:(listn n)]<[_:nat]nat>Cases l of 
-                         niln  => O
-                      | (consn n a niln) => O
-                      | (consn n a (consn m b l)) => (plus n m)
-                      end.
-
-Type [n:nat][l:(listn n)]Cases l of 
-                         niln  => O
-                      | (consn n a niln) => O
-                      | (consn n a (consn m b l)) => (plus n m)
-                      end.
-
-
-Type [A:Set][n:nat][l:(Listn A n)]<[_:nat]nat>Cases l of 
-                         Niln   => O
-                      | (Consn n a Niln) => O
-                      | (Consn n a (Consn m b l)) => (plus n m)
-                      end.
-
-Type [A:Set][n:nat][l:(Listn A n)]Cases l of 
-                         Niln   => O
-                      | (Consn n a Niln) => O
-                      | (Consn n a (Consn m b l)) => (plus n m)
-                      end.
-
-(*
-Type [A:Set][n:nat][l:(Listn A n)]
-                   <[_:nat](Listn A O)>Cases l of 
-                         (Niln  as b) => b
-                      | (Consn  n a (Niln  as b))=> (Niln A)
-                      | (Consn  n a (Consn m b l)) => (Niln A)
-                      end.
-
-Type [A:Set][n:nat][l:(Listn A n)]
-                    Cases l of 
-                         (Niln  as b) => b
-                      | (Consn  n a (Niln  as b))=> (Niln A)
-                      | (Consn  n a (Consn m b l)) => (Niln A)
-                      end.
-*)
-(******** This example rises an error unconstrained_variables!
-Type [A:Set][n:nat][l:(Listn A n)]
-                    Cases l of 
-                         (Niln  as b) => (Consn A O O b)
-                      | ((Consn  n a Niln) as L) =>  L 
-                      | (Consn  n a _)  =>  (Consn A O O (Niln A))
-                      end.
-**********)
-
-(* To test tratement of as-patterns in depth *)
-Type [A:Set] [l:(List A)]
-                    Cases l of 
-                         (Nil  as b) => (Nil A)
-                      | ((Cons a Nil)  as L) => L
-                      | ((Cons a (Cons b m)) as L) => L
-                      end.
-
-
-Type [n:nat][l:(listn n)]
-             <[_:nat](listn n)>Cases l of 
-                         niln  => l 
-                      | (consn n a c) => l
-                      end.
-Type [n:nat][l:(listn n)]
-                      Cases l of 
-                         niln  => l 
-                      | (consn n a c) => l
-                      end.
-
-
-Type [n:nat][l:(listn n)]
-             <[_:nat](listn n)>Cases l of 
-                         (niln as b) => l 
-                      |  _  => l
-                      end.
-
-
-Type [n:nat][l:(listn n)]
-                     Cases l of 
-                         (niln as b) => l 
-                      |  _  => l
-                      end.
-
-Type [n:nat][l:(listn n)]
-             <[_:nat](listn n)>Cases l of 
-                         (niln as b) => l
-                      |  x  => l
-                      end.
-
-
-Type [A:Set][n:nat][l:(Listn A n)]
-                       Cases l of 
-                         (Niln  as b) => l 
-                      |   _ => l
-                      end.
-
-Type [A:Set][n:nat][l:(Listn A n)]
-             <[_:nat](Listn A n)>Cases l of 
-                         Niln  => l 
-                      | (Consn  n a Niln) => l
-                      | (Consn  n a (Consn  m b c)) => l 
-                      end.
-
-Type [A:Set][n:nat][l:(Listn A n)]
-                      Cases l of 
-                         Niln  => l 
-                      | (Consn  n a Niln) => l
-                      | (Consn  n a (Consn  m b c)) => l 
-                      end.
-
-Type [A:Set][n:nat][l:(Listn A n)]
-             <[_:nat](Listn A n)>Cases l of 
-                         (Niln as b) => l 
-                      | (Consn  n a (Niln as b)) => l
-                      | (Consn  n a (Consn  m b _)) => l 
-                      end.
-
-Type [A:Set][n:nat][l:(Listn A n)]
-                     Cases l of 
-                         (Niln as b) => l 
-                      | (Consn  n a (Niln as b)) => l
-                      | (Consn  n a (Consn  m b _)) => l 
-                      end.
-
-
-Type <[_:nat]nat>Cases (niln) of 
-                         niln  => O
-                      | (consn n a niln) => O
-                      | (consn n a (consn m b l)) => (plus n m)
-                      end.
-
-
-Type               Cases (niln) of 
-                         niln  => O
-                      | (consn n a niln) => O
-                      | (consn n a (consn m b l)) => (plus n m)
-                      end.
-
-Type <[_,_:nat]nat>Cases (LeO O) of 
-                         (LeO x)  => x
-                      | (LeS n m h) => (plus n m) 
-                      end.
-
-
-Type               Cases (LeO O) of 
-                         (LeO x)  => x
-                      | (LeS n m h) => (plus n m) 
-                      end.
-
-Type [n:nat][l:(Listn nat n)]
-                     <[_:nat]nat>Cases l of 
-                         Niln  => O
-                      | (Consn n a l) => O
-                      end.
-
-
-Type [n:nat][l:(Listn nat n)]
-                      Cases l of 
-                         Niln  => O
-                      | (Consn n a l) => O
-                      end.
-
-
-Type                Cases (Niln nat) of 
-                         Niln  => O
-                      | (Consn n a l) => O
-                      end.
-
-Type <[_:nat]nat>Cases (LE_n O) of 
-                         LE_n   => O 
-                      | (LE_S m h) => O
-                      end.
-
-
-Type               Cases (LE_n O) of 
-                         LE_n   => O 
-                      | (LE_S m h) => O
-                      end.
-
-
-
-Type               Cases (LE_n O) of 
-                         LE_n   => O 
-                      | (LE_S m h) => O
-                      end.
-
-
-
-Type <[_:nat]nat>Cases (niln ) of 
-                         niln   => O
-                      | (consn  n a niln) => n
-                      | (consn  n a (consn  m b l)) => (plus n m)
-                      end.
-
-Type               Cases (niln ) of 
-                         niln   => O
-                      | (consn  n a niln) => n
-                      | (consn  n a (consn  m b l)) => (plus n m)
-                      end.
-
-
-Type <[_:nat]nat>Cases (Niln nat) of 
-                         Niln  => O
-                      | (Consn  n a Niln) => n
-                      | (Consn   n a (Consn  m b l)) => (plus n m)
-                      end.
-
-Type                Cases (Niln nat) of 
-                         Niln  => O
-                      | (Consn  n a Niln) => n
-                      | (Consn   n a (Consn  m b l)) => (plus n m)
-                      end.
-
-
-Type <[_,_:nat]nat>Cases (LeO O) of 
-                         (LeO x)  => x
-                      | (LeS n m (LeO x)) => (plus x m)
-                      | (LeS n m (LeS x y h)) => (plus n x)
-                      end.
-
-
-Type                 Cases (LeO O) of 
-                         (LeO x)  => x
-                      | (LeS n m (LeO x)) => (plus x m)
-                      | (LeS n m (LeS x y h)) => (plus n x)
-                      end.
-
-
-Type <[_,_:nat]nat>Cases (LeO O) of 
-                         (LeO x)  => x
-                      | (LeS n m (LeO x)) => (plus x m)
-                      | (LeS n m (LeS x y h)) => m
-                      end.
-
-Type                Cases (LeO O) of 
-                         (LeO x)  => x
-                      | (LeS n m (LeO x)) => (plus x m)
-                      | (LeS n m (LeS x y h)) => m
-                      end.
-
-
-Type [n,m:nat][h:(Le n m)]
-                    <[_,_:nat]nat>Cases h of 
-                         (LeO x)  => x
-                      | x => O
-                      end.
-
-Type [n,m:nat][h:(Le n m)]
-                     Cases h of 
-                         (LeO x)  => x
-                      | x => O
-                      end.
-
-
-Type [n,m:nat][h:(Le n m)]
-                    <[_,_:nat]nat>Cases h of 
-                        (LeS n m h)  => n
-                      | x => O
-                      end.
-
-
-Type [n,m:nat][h:(Le n m)]
-                      Cases h of 
-                        (LeS n m h)  => n
-                      | x => O
-                      end.
-
-
-Type    [n,m:nat][h:(Le n m)]
-  <[_,_:nat]nat*nat>Cases h of
-                    (LeO n) => (O,n)
-                   |(LeS n m _) => ((S n),(S m))
-                   end.
-
-
-Type    [n,m:nat][h:(Le n m)]
-                  Cases h of
-                    (LeO n) => (O,n)
-                   |(LeS n m _) => ((S n),(S m))
-                   end.
-
-
-Fixpoint F [n,m:nat; h:(Le n m)] : (Le n (S m)) :=
- <[n,m:nat](Le n (S m))>Cases h  of 
-                (LeO m') => (LeO (S m'))
-              | (LeS n' m' h') => (LeS n' (S m') (F n' m' h'))
-        end.
-
-Reset F.
-
-Fixpoint F [n,m:nat; h:(Le n m)] :(Le n (S m)) :=
-  <[n,m:nat](Le n (S m))>Cases h of
-                           (LeS n m h) => (LeS n (S m) (F n m h))
-                         | (LeO m) => (LeO (S m)) 
-                        end.
-
-(* Rend la longueur de la liste *)
-Definition length1:= [n:nat] [l:(listn n)]
-        <[_:nat]nat>Cases l of 
-                     (consn n _ (consn m _ _)) => (S (S m))
-                    |(consn n _ _) => (S O)
-                    | _ => O
-             end.
-
-Reset length1.
-Definition length1:= [n:nat] [l:(listn n)]
-                    Cases l of 
-                     (consn n _ (consn m _ _)) => (S (S m))
-                    |(consn n _ _) => (S O)
-                    | _ => O
-                    end.
-
-
-Definition length2:= [n:nat] [l:(listn n)]
-        <[_:nat]nat>Cases l of 
-                     (consn n _ (consn m _ _)) => (S (S m))
-                    |(consn n _ _) => (S n)
-                    | _ => O
-             end.
-
-Reset length2.
-
-Definition length2:= [n:nat] [l:(listn n)]
-                   Cases l of 
-                     (consn n _ (consn m _ _)) => (S (S m))
-                    |(consn n _ _) => (S n)
-                    | _ => O
-                   end.
-
-Definition length3 :=
-[n:nat][l:(listn n)]
-        <[_:nat]nat>Cases l of 
-                     (consn n _ (consn m _ l)) => (S n)
-                    |(consn n _ _) => (S O)
-                    | _  => O
-                   end.
-
-
-Reset length3.
-
-Definition length3 :=
-[n:nat][l:(listn n)]
-                   Cases l of 
-                     (consn n _ (consn m _ l)) => (S n)
-                    |(consn n _ _) => (S O)
-                    | _  => O
-                   end.
-
- 
-Type <[_,_:nat]nat>Cases (LeO O) of 
-                        (LeS n m h)  =>(plus n m)
-                      | x => O
-                      end.
-Type              Cases (LeO O) of 
-                        (LeS n m h)  =>(plus n m)
-                      | x => O
-                      end.
-
-Type [n,m:nat][h:(Le n m)]<[_,_:nat]nat>Cases h of 
-                         (LeO x)  => x
-                      | (LeS n m (LeO x)) => (plus x m)
-                      | (LeS n m (LeS x y h)) =>(plus n (plus m (plus x y)))
-                      end.
-
-
-Type [n,m:nat][h:(Le n m)]Cases h of 
-                         (LeO x)  => x
-                      | (LeS n m (LeO x)) => (plus x m)
-                      | (LeS n m (LeS x y h)) =>(plus n (plus m (plus x y)))
-                      end.
-
-Type <[_,_:nat]nat>Cases (LeO O) of 
-                         (LeO x)  => x
-                      | (LeS n m (LeO x)) => (plus x m)
-                      | (LeS n m (LeS x y h)) =>(plus n (plus m (plus x y)))
-                      end.
-
-Type                 Cases (LeO O) of 
-                         (LeO x)  => x
-                      | (LeS n m (LeO x)) => (plus x m)
-                      | (LeS n m (LeS x y h)) =>(plus n (plus m (plus x y)))
-                      end.
-
-
-Type <[_:nat]nat>Cases (LE_n O) of 
-                         LE_n   => O
-                      | (LE_S m LE_n) => (plus O m)
-                      | (LE_S m (LE_S y h)) => (plus O m)
-                      end.
-
-
-Type                Cases (LE_n O) of 
-                         LE_n   => O
-                      | (LE_S m LE_n) => (plus O m)
-                      | (LE_S m (LE_S y h)) => (plus O m)
-                      end.
-
-
-Type [n,m:nat][h:(Le n m)]              Cases h of 
-                                                x => x 
-                                          end.
-
-Type [n,m:nat][h:(Le n m)]<[_,_:nat]nat>Cases h of 
-                                               (LeO n) => n
-                                              |   x => O
-                                          end.
-Type [n,m:nat][h:(Le n m)] Cases h of 
-                               (LeO n) => n
-                             |   x => O
-                            end.
-
-
-Type [n:nat]<[_:nat]nat->nat>Cases niln of 
-                         niln  => [_:nat]O
-                      | (consn n a niln) => [_:nat]O
-                      | (consn n a (consn m b l)) => [_:nat](plus n m)
-                      end.
-
-
-Type [n:nat]         Cases niln of 
-                         niln  => [_:nat]O
-                      | (consn n a niln) => [_:nat]O
-                      | (consn n a (consn m b l)) => [_:nat](plus n m)
-                      end.
-
-Type [A:Set][n:nat][l:(Listn A n)]
-                  <[_:nat]nat->nat>Cases l of 
-                         Niln  => [_:nat]O
-                      | (Consn  n a Niln) =>  [_:nat] n
-                      | (Consn  n a (Consn  m b l)) => [_:nat](plus n m)
-                      end.
-
-Type [A:Set][n:nat][l:(Listn A n)]
-                        Cases l of 
-                         Niln  => [_:nat]O
-                      | (Consn  n a Niln) =>  [_:nat] n
-                      | (Consn  n a (Consn  m b l)) => [_:nat](plus n m)
-                      end.
-
-(* Alsos tests for multiple _ patterns *)
-Type [A:Set][n:nat][l:(Listn A n)]
-                  <[n:nat](Listn A n)>Cases l of 
-                        (Niln as b) => b
-                      | ((Consn _ _ _ ) as b)=>  b
-                      end.
-
-(** Horrible error message! 
-
-Type [A:Set][n:nat][l:(Listn A n)]
-                        Cases l of 
-                        (Niln as b) => b
-                      | ((Consn _ _ _ ) as b)=>  b
-                      end.
-******)
-
-Type   <[n:nat](listn  n)>Cases niln of 
-               (niln as b) => b
-          | ((consn _ _ _ ) as b)=>  b
-          end.
-
-
-Type   <[n:nat](listn  n)>Cases niln of 
-               (niln as b) => b
-          |    x  =>  x
-          end.
-
-Type [n,m:nat][h:(LE n m)]<[_:nat]nat->nat>Cases h  of 
-                         LE_n   => [_:nat]n
-                      | (LE_S  m LE_n) => [_:nat](plus n m)
-                      | (LE_S  m (LE_S y h)) => [_:nat](plus m y )
-                      end.
-Type [n,m:nat][h:(LE n m)]Cases h  of 
-                         LE_n   => [_:nat]n
-                      | (LE_S  m LE_n) => [_:nat](plus n m)
-                      | (LE_S  m (LE_S y h)) => [_:nat](plus m y )
-                      end.
-
-
-Type [n,m:nat][h:(LE n m)]
-    <[_:nat]nat>Cases h  of 
-        LE_n   => n
-      | (LE_S m  LE_n ) => (plus n m)
-      | (LE_S  m (LE_S  y  LE_n )) => (plus (plus n m) y)
-      | (LE_S  m (LE_S  y (LE_S  y' h))) => (plus (plus n m) (plus y y'))
-                      end.
-
-
-
-Type [n,m:nat][h:(LE n m)]
-       Cases h  of 
-        LE_n   => n
-      | (LE_S m  LE_n ) => (plus n m)
-      | (LE_S  m (LE_S  y  LE_n )) => (plus (plus n m) y)
-      | (LE_S  m (LE_S  y (LE_S  y' h))) => (plus (plus n m) (plus y y'))
-                      end.
-
-
-Type [n,m:nat][h:(LE n m)]<[_:nat]nat>Cases h  of 
-                        LE_n   => n
-                      | (LE_S m LE_n) => (plus n m)
-                      | (LE_S  m (LE_S y h)) => (plus (plus n m) y)
-                      end.
-
-
-Type [n,m:nat][h:(LE n m)]Cases h  of 
-                        LE_n   => n
-                      | (LE_S m LE_n) => (plus n m)
-                      | (LE_S  m (LE_S y h)) => (plus (plus n m) y)
-                      end.
-
-Type [n,m:nat]
-                    <[_,_:nat]nat>Cases (LeO O) of 
-                        (LeS n m h)  =>(plus n m)
-                      | x => O
-                      end.
-
-Type [n,m:nat]
-                      Cases (LeO O) of 
-                        (LeS n m h)  =>(plus n m)
-                      | x => O
-                      end.
-
-Parameter test : (n:nat){(le O n)}+{False}.
-Type  [n:nat]<nat>Cases (test n) of
-                        (left _) => O 
-                        | _ => O end.
-
-
-Type  [n:nat]   <nat> Cases (test n) of
-                          (left _) => O 
-                        | _ => O end.
-
-Type  [n:nat]Cases (test n) of
-                          (left _) => O 
-                        | _ => O end.
-
-Parameter compare : (n,m:nat)({(lt n m)}+{n=m})+{(gt n m)}.
-Type <nat>Cases (compare O O) of
-               (* k<i *)  (inleft (left _)) => O
-            |  (* k=i *)  (inleft  _)  => O
-            |  (* k>i *)  (inright  _) => O end.
-
-Type    Cases (compare O O) of
-               (* k<i *)  (inleft (left _)) => O
-            |  (* k=i *)  (inleft  _)  => O
-            |  (* k>i *)  (inright  _) => O end.
-
-
-
-CoInductive SStream [A:Set]  : (nat->A->Prop)->Set :=
-scons  : 
-  (P:nat->A->Prop)(a:A)(P O a)->(SStream A [n:nat](P (S n)))->(SStream A P).
-Parameter B : Set.
-
-Type 
-  [P:nat->B->Prop][x:(SStream B P)]<[_:nat->B->Prop]B>Cases x of
-     (scons _ a _ _) => a  end.
-
-
-Type 
-  [P:nat->B->Prop][x:(SStream B P)] Cases x of
-     (scons _ a _ _) => a  end.
-
-Type <nat*nat>Cases (O,O) of  (x,y) => ((S x),(S y)) end.
-Type <nat*nat>Cases (O,O) of  ((x as b), y) => ((S x),(S y)) end.
-Type <nat*nat>Cases (O,O) of  (pair x y) => ((S x),(S y)) end.
-
-Type Cases (O,O) of  (x,y) => ((S x),(S y)) end.
-Type Cases (O,O) of  ((x as b), y) => ((S x),(S y)) end.
-Type Cases (O,O) of  (pair x y) => ((S x),(S y)) end.
-
-
-
-Parameter concat : (A:Set)(List A) ->(List A) ->(List A).
-
-Type <(List nat)>Cases (Nil nat) (Nil nat) of 
-                 (Nil as b)  x  => (concat nat b x)
-              | ((Cons _ _) as d) (Nil as c) => (concat nat d c)
-              |  _ _ => (Nil nat)
-              end.
-Type Cases (Nil nat) (Nil nat) of 
-           (Nil as b)  x  => (concat nat b x)
-       | ((Cons _ _) as d) (Nil as c) => (concat nat d c)
-       |  _ _ => (Nil nat)
-       end.
-
-
-Inductive redexes : Set :=
-    VAR : nat -> redexes
-  | Fun : redexes -> redexes
-  | Ap  : bool -> redexes -> redexes -> redexes.
-
-Fixpoint regular [U:redexes] : Prop := <Prop>Cases U of
-  (VAR n) => True
-| (Fun V) => (regular V)
-| (Ap true ((Fun _) as V)  W) => (regular V) /\ (regular W)
-| (Ap true _ W) => False
-| (Ap false V W) => (regular V) /\ (regular W) 
-end.
-
-
-Type [n:nat]Cases n of O => O | (S ((S n) as V)) => V | _ => O end.
-
-Reset concat.
-Parameter concat :(n:nat) (listn n) -> (m:nat) (listn m)-> (listn (plus n m)).
-Type [n:nat][l:(listn n)][m:nat][l':(listn m)] 
- <[n,_:nat](listn (plus n m))>Cases l l' of 
-                 niln  x => x
-              | (consn n a l'') x =>(consn (plus n m) a (concat n l'' m x))
-               end.
-
-Type [x,y,z:nat]
-        [H:x=y]
-         [H0:y=z]<[_:nat]x=z>Cases H of refl_equal => 
-                          <[n:nat]x=n>Cases H0 of refl_equal => H
-                                             end
-                                       end.
-
-Type [h:False]<False>Cases h of end.
-
-Type [h:False]<True>Cases h of end.
-
-Definition is_zero := [n:nat]Cases n of O => True | _ => False end.
-
-Type [n:nat][h:O=(S n)]<[n:nat](is_zero n)>Cases h of refl_equal => I end.
-
-Definition disc : (n:nat)O=(S n)->False :=
-  [n:nat][h:O=(S n)]
-      <[n:nat](is_zero n)>Cases h of refl_equal => I end.
-
-Definition nlength3 := [n:nat] [l: (listn n)]
-                         Cases l of 
-                            niln  => O
-                         |  (consn O  _ _)  => (S O)
-                         |  (consn (S n)  _ _) => (S (S n))
-                         end.
-
-(* == Testing strategy elimintation predicate  synthesis == *)
-Section titi.
-Variable h:False.
-Type Cases O of 
-          O  => O
-       |  _  => (Except h)
-       end.
-End titi.
-
-Type Cases niln of 
-    (consn _ a niln) => a
- |  (consn n _ x)    => O
- |   niln  => O
- end.
-
-
-
-Inductive wsort : Set := ws : wsort | wt : wsort.
-Inductive TS : wsort->Set := 
-   id :(TS ws) 
-| lift:(TS ws)->(TS ws).
-
-Type [b:wsort][M:(TS b)][N:(TS b)]
- Cases   M   N of   
-  (lift M1)   id => False 
- | _ _ => True 
- end.
-
-
-
-(* ===================================================================== *)
-(* To test pattern matching over a non-dependent inductive type, but     *)
-(* having constructors with some arguments that depend on others         *)
-(* I.e. to test manipulation of elimination predicate                    *)
-(* ===================================================================== *)
-
-
-Parameter LTERM : nat -> Set.
-Mutual Inductive TERM : Type :=
-	  var : TERM
-	| oper : (op:nat) (LTERM op) -> TERM.
-
-Parameter t1, t2:TERM.
-
-Type Cases t1 t2 of 
-   var   var  => True
-
- | (oper op1 l1)  (oper op2 l2) => False
- | _ _ => False 
- end. 
-Reset LTERM.
-
-
-
-Require Peano_dec.
-Parameter n:nat.
-Definition eq_prf := (EXT m | n=m).
-Parameter p:eq_prf .
-
-Type Cases p of
-     (exT_intro c eqc) =>
-          Cases (eq_nat_dec c n) of
-            (right _) => (refl_equal ? n)
-           |(left y) (* c=n*) => (refl_equal ? n) 
-          end
-     end.
-
-
-Parameter ordre_total : nat->nat->Prop.
-
-Parameter N_cla:(N:nat){N=O}+{N=(S O)}+{(ge N (S (S O)))}.
-
-Parameter exist_U2:(N:nat)(ge N (S (S O)))->
-                      {n:nat|(m:nat)(lt O m)/\(le m N)
-                             /\(ordre_total n m)                   
-                             /\(lt O n)/\(lt n N)}.
-
-Type [N:nat](Cases (N_cla N) of
-                         (inright H)=>(Cases (exist_U2 N H) of
-                                               (exist a b)=>a
-                                       end)
-                        |   _       => O
-                       end).
-
-
-
-(* ============================================== *)
-(*     To test compilation of dependent case      *)
-(*  Nested patterns                               *)
-(* ============================================== *)
-
-(* == To test that terms named with AS are correctly absolutized before
-      substitution in rhs   == *)
-
-Type [n:nat]<[n:nat]nat>Cases (n) of 
-          O  => O
-       |  (S O)  => O
-       |  ((S (S n1)) as N)  => N
-      end.
-
-(* ========= *)
-
-Type <[n:nat][_:(listn n)]Prop>Cases niln of 
-                         niln => True
-                       | (consn (S O) _ _) => False
-                       | _ => True end.
-
-Type <[n:nat][_:(listn n)]Prop>Cases niln of 
-                         niln => True
-                       | (consn (S (S O)) _ _) => False
-                       | _ => True end.
-
-
-Type <[n,m:nat][h:(Le n m)]nat>Cases (LeO O) of 
-                         (LeO _) => O
-                       | (LeS (S x) _ _) => x
-                       | _ => (S O) end.
-
-Type <[n,m:nat][h:(Le n m)]nat>Cases (LeO O) of 
-                         (LeO _) => O
-                       | (LeS (S x)  (S y) _) => x
-                       | _ => (S O) end.
-
-Type <[n,m:nat][h:(Le n m)]nat>Cases (LeO O) of 
-                         (LeO _) => O
-                       | (LeS ((S x) as b)  (S y) _) => b
-                       | _ => (S O) end.
-
-
-
-Parameter ff: (n,m:nat)~n=m -> ~(S n)=(S m).
-Parameter discr_r : (n:nat) ~(O=(S n)).
-Parameter discr_l : (n:nat) ~((S n)=O).
-
-Type 
-[n:nat] 
-  <[n:nat]n=O\/~n=O>Cases n of 
-      O     => (or_introl ? ~O=O (refl_equal ? O))      
-   |  (S x) => (or_intror (S x)=O ? (discr_l x))
-  end.
-
-
-Fixpoint eqdec [n:nat] : (m:nat) n=m \/ ~n=m := 
-[m:nat]
- <[n,m:nat] n=m \/ ~n=m>Cases n m of
-      O   O   => (or_introl ? ~O=O (refl_equal ? O))
-
-   |  O (S x) => (or_intror O=(S x) ? (discr_r x))
-
-   | (S x) O  => (or_intror ? ~(S x)=O (discr_l x))
-
-   | (S x) (S y) =>  
-      <(S x)=(S y)\/~(S x)=(S y)>Cases (eqdec x y) of
-        (or_introl h) => (or_introl  ? ~(S x)=(S y) (f_equal nat nat S x y h))
-      | (or_intror h) => (or_intror (S x)=(S y) ? (ff x y h))   
-      end
- end.
-
-Reset eqdec.
-
-Fixpoint eqdec [n:nat] : (m:nat) n=m \/ ~n=m := 
-<[n:nat] (m:nat)n=m \/ ~n=m>Cases n  of
-    O  => [m:nat] <[m:nat]O=m\/~O=m>Cases m of 
-                     O    => (or_introl ? ~O=O (refl_equal nat O))
-                   |(S x) => (or_intror O=(S x) ?  (discr_r x))
-                  end
-  | (S x) => [m:nat] 
-    <[m:nat](S x)=m\/~(S x)=m>Cases m of  
-        O    => (or_intror (S x)=O ? (discr_l x))
-     | (S y) =>  
-         <(S x)=(S y)\/~(S x)=(S y)>Cases (eqdec x y) of
-            (or_introl h) => (or_introl ? ~(S x)=(S y) (f_equal ? ? S x y h))
-          | (or_intror h) => (or_intror (S x)=(S y) ? (ff x y h))   
-         end
-    end
- end.
-
-
-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 a y) as b) =>  (or_intror (empty (S n) b) ? (inv_empty n a y))
-  end.
-
-Reset ff.
-Parameter ff: (n,m:nat)~n=m -> ~(S n)=(S m).
-Parameter discr_r : (n:nat) ~(O=(S n)).
-Parameter discr_l : (n:nat) ~((S n)=O).
-
-Type 
-[n:nat] 
-  <[n:nat]n=O\/~n=O>Cases n of 
-      O     => (or_introl ? ~O=O (refl_equal ? O))      
-   |  (S x) => (or_intror (S x)=O ? (discr_l x))
-  end.
-
-
-Fixpoint eqdec [n:nat] : (m:nat) n=m \/ ~n=m := 
-[m:nat]
- <[n,m:nat] n=m \/ ~n=m>Cases n m of
-      O   O   => (or_introl ? ~O=O (refl_equal ? O))
-
-   |  O (S x) => (or_intror O=(S x) ? (discr_r x))
-
-   | (S x) O  => (or_intror ? ~(S x)=O (discr_l x))
-
-   | (S x) (S y) =>  
-      <(S x)=(S y)\/~(S x)=(S y)>Cases (eqdec x y) of
-        (or_introl h) => (or_introl  ? ~(S x)=(S y) (f_equal nat nat S x y h))
-      | (or_intror h) => (or_intror (S x)=(S y) ? (ff x y h))   
-      end
- end.
-Reset eqdec.
-
-Fixpoint eqdec [n:nat] : (m:nat) n=m \/ ~n=m := 
-<[n:nat] (m:nat)n=m \/ ~n=m>Cases n  of
-    O  => [m:nat] <[m:nat]O=m\/~O=m>Cases m of 
-                     O    => (or_introl ? ~O=O (refl_equal nat O))
-                   |(S x) => (or_intror O=(S x) ?  (discr_r x))
-                  end
-  | (S x) => [m:nat] 
-    <[m:nat](S x)=m\/~(S x)=m>Cases m of  
-        O    => (or_intror (S x)=O ? (discr_l x))
-     | (S y) =>  
-         <(S x)=(S y)\/~(S x)=(S y)>Cases (eqdec x y) of
-            (or_introl h) => (or_introl ? ~(S x)=(S y) (f_equal ? ? S x y h))
-          | (or_intror h) => (or_intror (S x)=(S y) ? (ff x y h))   
-         end
-    end
- end.
-
-
-(* ================================================== *)
-(* Pour tester parametres                             *)
-(* ================================================== *)
-
-
-Inductive Empty [A:Set] : (List A)-> Prop := 
-  intro_Empty: (Empty A (Nil A)).
-
-Parameter inv_Empty : (A:Set)(a:A)(x:(List A)) ~(Empty A (Cons A a x)).
-
-
-Type
-  <[l:(List nat)](Empty nat l) \/ ~(Empty nat l)>Cases (Nil nat) of 
-        Nil   =>  (or_introl ? ~(Empty nat (Nil nat)) (intro_Empty nat))
-   |   (Cons a y)  =>  (or_intror (Empty nat (Cons nat a y)) ? 
-                                   (inv_Empty nat a y))
-  end.
-
-
-(* ================================================== *)
-(* Sur les listes                                     *)
-(* ================================================== *)
-
-
-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 a y) as b) =>  (or_intror (empty (S n) b) ? (inv_empty n a y))
-  end.
-
-(* ===================================== *)
-(*   Test parametros:                    *)
-(* ===================================== *)
-
-Inductive eqlong : (List nat)-> (List nat)-> Prop :=
- eql_cons : (n,m:nat)(x,y:(List nat)) 
-            (eqlong x y) -> (eqlong (Cons nat n x) (Cons nat m y))
-| eql_nil :  (eqlong (Nil nat) (Nil nat)).
-
-
-Parameter V1 : (eqlong (Nil nat) (Nil nat))\/ ~(eqlong (Nil nat) (Nil nat)).
-Parameter V2 : (a:nat)(x:(List nat))
-      (eqlong (Nil nat) (Cons nat a x))\/ ~(eqlong (Nil nat)(Cons nat a x)).
-Parameter V3 : (a:nat)(x:(List nat))
-      (eqlong  (Cons nat a x)  (Nil nat))\/ ~(eqlong (Cons nat a x) (Nil nat)).
-Parameter V4 : (a:nat)(x:(List nat))(b:nat)(y:(List nat))
-      (eqlong  (Cons nat a x)(Cons nat b y))
-        \/ ~(eqlong (Cons nat a x) (Cons nat b y)).
-
-Type
- <[x,y:(List nat)](eqlong x y)\/~(eqlong x y)>Cases (Nil nat) (Nil nat) of
-      Nil Nil   => V1
-   |  Nil (Cons a x)  => (V2 a x)
-   |  (Cons a x)  Nil => (V3 a x)
-   | (Cons a x)  (Cons b y)  => (V4 a x b y)
- end.
-
-
-Type
-[x,y:(List nat)]
- <[x,y:(List nat)](eqlong x y)\/~(eqlong x y)>Cases x y of
-      Nil Nil   => V1
-   |  Nil (Cons a x)  => (V2 a x)
-   |  (Cons a x)  Nil => (V3 a x)
-   | (Cons a x)  (Cons b y)  => (V4 a x b y)
- end.
-
- 
-(* ===================================== *)
-
-Inductive Eqlong : (n:nat) (listn n)-> (m:nat) (listn m)-> Prop :=
- Eql_cons : (n,m:nat )(x:(listn n))(y:(listn m)) (a,b:nat) 
-            (Eqlong n x m y) 
-             ->(Eqlong (S n) (consn n a x) (S m) (consn m b y))
-| Eql_niln :  (Eqlong O niln O niln).
-
-
-Parameter W1 : (Eqlong O niln O niln)\/ ~(Eqlong O niln O niln).
-Parameter W2 : (n,a:nat)(x:(listn n)) 
-  (Eqlong O niln (S n)(consn n a x)) \/ ~(Eqlong  O niln (S n) (consn n a x)).
-Parameter W3 : (n,a:nat)(x:(listn n)) 
- (Eqlong (S n) (consn n a x)  O niln) \/ ~(Eqlong (S n) (consn n a x)  O niln).
-Parameter W4 : (n,a:nat)(x:(listn n)) (m,b:nat)(y:(listn m)) 
-      (Eqlong  (S n)(consn n a x) (S m) (consn m b y))
-        \/ ~(Eqlong (S n)(consn n a x) (S m) (consn m b y)).
-
-Type
- <[n:nat][x:(listn n)][m:nat][y:(listn m)]
-     (Eqlong n x m y)\/~(Eqlong n x m y)>Cases niln  niln  of
-      niln niln   => W1
-   |  niln (consn n a x)  => (W2 n a x)
-   |  (consn n a x)  niln => (W3 n a x)
-   | (consn n a x)  (consn m b y)  => (W4 n a x m b y)
- end.
-
-
-Type 
-[n,m:nat][x:(listn n)][y:(listn m)]
- <[n:nat][x:(listn n)][m:nat][y:(listn m)]
-     (Eqlong n x m y)\/~(Eqlong n x m y)>Cases x y of
-      niln niln   => W1
-   |  niln (consn n a x)  => (W2 n a x)
-   |  (consn n a x)  niln => (W3 n a x)
-   | (consn n a x)  (consn m b y)  => (W4 n a x m b y)
- end.
-
-
-Parameter Inv_r : (n,a:nat)(x:(listn n)) ~(Eqlong O niln (S n) (consn n a x)).
-Parameter Inv_l : (n,a:nat)(x:(listn n)) ~(Eqlong (S n) (consn n a x) O niln).
-Parameter Nff : (n,a:nat)(x:(listn n)) (m,b:nat)(y:(listn m)) 
-               ~(Eqlong n x m y)
-                -> ~(Eqlong (S n) (consn n a x) (S m) (consn m b y)).
-
-
-
-Fixpoint Eqlongdec [n:nat; x:(listn n)] : (m:nat)(y:(listn m))
-                                           (Eqlong n x m y)\/~(Eqlong n x m y)
-:= [m:nat][y:(listn m)]
- <[n:nat][x:(listn n)][m:nat][y:(listn m)]
-     (Eqlong n x m y)\/~(Eqlong n x m y)>Cases x y of
-      niln niln   => (or_introl ? ~(Eqlong O niln O niln)  Eql_niln)
-
-   |  niln ((consn n a x) as L)  => 
-        (or_intror (Eqlong O niln (S n) L)  ? (Inv_r n a x))
-
-   | ((consn n a x) as L)  niln => 
-       (or_intror (Eqlong (S n) L O niln) ? (Inv_l n a x))
-
-
-   | ((consn n a x) as L1) ((consn m b y) as L2) =>
-     <(Eqlong (S n) L1 (S m) L2) \/~(Eqlong (S n) L1 (S m) L2)>
-      Cases (Eqlongdec n x m y) of
-        (or_introl h) => 
-           (or_introl  ? ~(Eqlong (S n) L1 (S m) L2)(Eql_cons n m x y a b h))
-      | (or_intror h) => 
-           (or_intror (Eqlong (S n) L1 (S m) L2) ? (Nff n a x  m b y h))   
-      end
- end.
-
-(* ============================================== *)
-(*     To test compilation of dependent case      *)
-(*      Multiple Patterns                         *)
-(* ============================================== *)
-Inductive skel: Type :=
-     PROP: skel
-   | PROD: skel->skel->skel.
-
-Parameter Can : skel -> Type.
-Parameter default_can : (s:skel) (Can s).
-
-Type  [s1,s2:skel]
-[s1,s2:skel]<[s1:skel][_:skel](Can s1)>Cases s1 s2 of
-  PROP PROP => (default_can PROP)
-| (PROD x y) PROP => (default_can (PROD x y))
-| (PROD x y) _ => (default_can (PROD x y))
-| PROP _ => (default_can PROP)
-end.
-
-(* to test bindings in nested Cases *)
-(* ================================ *)
-Inductive Pair : Set :=
-  pnil : Pair |
-  pcons : Pair -> Pair -> Pair.
-
-Type [p,q:Pair]Cases p of
-  (pcons _ x) => 
-     Cases q of 
-      (pcons _ (pcons _ x)) => True
-     |  _  => False
-     end
-|  _  => False
-end.
-
-
-Type [p,q:Pair]Cases p of
-  (pcons _ x) => 
-     Cases q of 
-      (pcons _ (pcons _ x)) => 
-          Cases q of 
-              (pcons _ (pcons _ (pcons _ x))) => x
-           | _ => pnil
-           end
-     |  _  => pnil
-     end
-|  _  => pnil
-end.
-
-Type  
-  [n:nat]
-         [l:(listn (S n))]
-           <[z:nat](listn (pred z))>Cases l of 
-                       niln  => niln
-                    |  (consn n _ l)  => 
-                           <[m:nat](listn m)>Cases l of 
-                                             niln => niln
-                                           | b => b
-                                           end
-                   end.
-
-
-
-(* Test de la syntaxe avec nombres *)
-Require Arith.
-Type [n]Cases n of 2 => true | _ => false end.
-
-Require ZArith.
-Type [n]Cases n of `0` => true | _ => false end.