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(*   Copyright Dominique Larchey-Wendling [*]                 *)
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(*                             [*] Affiliation LORIA -- CNRS  *)
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(*      This file is distributed under the terms of the       *)
(*         CeCILL v2 FREE SOFTWARE LICENSE AGREEMENT          *)
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Set Implicit Arguments.
Section fin_reif.
Variable (X : Type) (R : nat -> X -> Prop).
Fact fin_reif n : (forall i, i < n -> exists x, R i x)
-> exists s, forall i (Hi : i < n), R i (s i Hi).
End fin_reif.
Fact fin_reif_nat (R : nat -> nat -> Prop) n :
(forall i, i < n -> ex (R i)) -> exists s, forall i, i < n -> R i (s i).
Section bounded_search.

Theorem bounded_search m (P : nat -> Type) :
(forall n, n < m -> P n + (P n -> False))
-> { n : nat & (n < m) * P n }%type + { forall n, n < m -> P n -> False }.