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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(* ----                          Wf_compl.v                           ----*)
(* Author: Pierre Casteran.                                               *)
(*    LABRI, URA CNRS 1304,                                               *)
(*    Departement d'Informatique, Universite Bordeaux I,                  *)
(*    33405 Talence CEDEX,                                                *)
(*    e-mail:  casteran@labri.u-bordeaux.fr                               *)
(* Complements on well_founded Sets *)
Section Prop_induction.
Variable A : Set.
Variable R : A -> A -> Prop.
Hypothesis W : well_founded R.
Hint Resolve W: arith.

(* Specifications: *)
Lemma Prop_wfi :
forall P : A -> Prop,
(forall x : A, (forall y : A, R y x -> P y) -> P x) -> forall a : A, P a.