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diff --git a/contrib/field/LegacyField_Compl.v b/contrib/field/LegacyField_Compl.v
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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(* $Id$ *)
+
+Require Import List.
+
+Definition assoc_2nd :=
+  (fix assoc_2nd_rec (A:Type) (B:Set)
+                     (eq_dec:forall e1 e2:B, {e1 = e2} + {e1 <> e2})
+                     (lst:list (prod A B)) {struct lst} : 
+   B -> A -> A :=
+     fun (key:B) (default:A) =>
+       match lst with
+       | nil => default
+       | (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 mem :=
+  (fix mem (A:Set) (eq_dec:forall e1 e2:A, {e1 = e2} + {e1 <> e2}) 
+           (a:A) (l:list A) {struct l} : bool :=
+     match l with
+     | nil => false
+     | a1 :: l1 =>
+         match eq_dec a a1 with
+         | left _ => true
+         | right _ => mem A eq_dec a l1
+         end
+     end).