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(*   Copyright Dominique Larchey-Wendling *                 *)
(*                                                            *)
(*                             * 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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Require Import List.

Require Import Undecidability.Synthetic.Undecidability.

From Undecidability.ILL
  Require Import ILL CLL ill ill_cll ill_cll_restr.

Theorem rILL_rCLL_cf_PROVABILITY : rILL_cf_PROVABILITY ⪯ rCLL_cf_PROVABILITY.
Proof.
  apply reduces_dependent; exists.
  intros (Γ,A).
  exists (⟦Γ⟧,[A]::nil).
  apply S_ill_cll_restr_equiv.
Qed.