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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: Field_Compl.v,v 1.2.2.1 2004/07/16 19:30:17 herbelin Exp $ *)
+
+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))
+  end.
+
+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.
+
+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 field_rel_option [A:Type] : Type :=
+  | Field_None : (field_rel_option A)
+  | Field_Some : (A -> A -> A) -> (field_rel_option A).