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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
From Undecidability.Shared.Libs.DLW.Vec
From Undecidability.TRAKHTENBROT
Set Implicit Arguments.
(* * FSAT and FSAT over discrete model are equivalent *)
(* This equivalence and hence reduction most probably cannot be proved for infinite models, or at least the way it is proved in here *)
(* Satisfiability of A in a finite and decidable model implies satisfiability of A in a finite, decidable and discrete model, in fact in a model based on the finite type (pos n) *)

Theorem fo_discrete_removal Σ (A : fol_form Σ) :
fo_form_fin_dec_SAT A
-> exists n, fo_form_fin_discr_dec_SAT_in A (pos n).