1 files changed, 45 insertions, 46 deletions

diff --git a/contrib/field/Field_Compl.v b/contrib/field/Field_Compl.v
index aa3a991470..c90fea1ecc 100644
--- a/contrib/field/Field_Compl.v
+++ b/contrib/field/Field_Compl.v
@@ -8,55 +8,54 @@
 
 (* $Id$ *)
 
-Inductive listT [A:Type] : Type :=
-  nilT : (listT A) | consT : A->(listT A)->(listT A).
-
-Fixpoint appT [A:Type][l:(listT A)] : (listT A) -> (listT A) :=
-  [m:(listT A)]
-  Cases l of
-  | nilT => m 
-  | (consT a l1) => (consT A a (appT A l1 m))
+Inductive listT (A:Type) : Type :=
+  | nilT : listT A
+  | consT : A -> listT A -> listT A.
+
+Fixpoint appT (A:Type) (l m:listT A) {struct l} : listT A :=
+  match l with
+  | nilT => m
+  | consT a l1 => consT A a (appT A l1 m)
   end.
 
-Inductive prodT [A,B:Type] : Type :=
-  pairT: A->B->(prodT A B).
+Inductive prodT (A B:Type) : Type :=
+    pairT : A -> B -> prodT A B.
 
 Definition assoc_2nd :=
-Fix assoc_2nd_rec
-  {assoc_2nd_rec 
-   [A:Type;B:Set;eq_dec:(e1,e2:B){e1=e2}+{~e1=e2};lst:(listT (prodT A B))]
-   : B->A->A:=
-  [key:B;default:A]
-  Cases lst of
-  | nilT => default
-  | (consT (pairT v e) l) =>
-    (Cases (eq_dec e key) of
-    | (left _) => v
-    | (right _) => (assoc_2nd_rec A B eq_dec l key default)
-    end)
-  end}.
-
-Definition fstT [A,B:Type;c:(prodT A B)] :=
-  Cases c of
-  | (pairT a _) => a
-  end.
-
-Definition sndT [A,B:Type;c:(prodT A B)] :=
-  Cases c of
-  | (pairT _ a) => a
-  end.
+  (fix assoc_2nd_rec (A:Type) (B:Set)
+                     (eq_dec:forall e1 e2:B, {e1 = e2} + {e1 <> e2})
+                     (lst:listT (prodT A B)) {struct lst} : 
+   B -> A -> A :=
+     fun (key:B) (default:A) =>
+       match lst with
+       | nilT => default
+       | consT (pairT v e) l =>
+           match eq_dec e key with
+           | left _ => v
+           | right _ => assoc_2nd_rec A B eq_dec l key default
+           end
+       end).
+
+Definition fstT (A B:Type) (c:prodT A B) := match c with
+                                            | pairT a _ => a
+                                            end.
+
+Definition sndT (A B:Type) (c:prodT A B) := match c with
+                                            | pairT _ a => a
+                                            end.
 
 Definition mem :=
-Fix mem {mem [A:Set;eq_dec:(e1,e2:A){e1=e2}+{~e1=e2};a:A;l:(listT A)] : bool :=
-  Cases l of
-  | nilT => false
-  | (consT a1 l1) =>
-    Cases (eq_dec a a1) of
-    | (left _) => true
-    | (right _) => (mem A eq_dec a l1)
-    end
-  end}.
-
-Inductive option [A:Type] : Type :=
-  | None : (option A)
-  | Some : (A -> A -> A) -> (option A).
+  (fix mem (A:Set) (eq_dec:forall e1 e2:A, {e1 = e2} + {e1 <> e2}) 
+           (a:A) (l:listT A) {struct l} : bool :=
+     match l with
+     | nilT => false
+     | consT a1 l1 =>
+         match eq_dec a a1 with
+         | left _ => true
+         | right _ => mem A eq_dec a l1
+         end
+     end).
+
+Inductive option (A:Type) : Type :=
+  | None : option A
+  | Some : (A -> A -> A) -> option A.
\ No newline at end of file