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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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From Undecidability.Shared.Libs.DLW.Utils
Set Implicit Arguments.

Theorem exists_dec_fin_t X (P Q : X -> Prop)
(Pdec : forall x, { P x } + { ~ P x })
(HQ : fin_t Q)
(HPQ : forall x, P x -> Q x) :
{ exists x, P x } + { ~ exists x, P x }.