Require Import List.

Require Import Undecidability.Synthetic.Undecidability.
Require Import Undecidability.Synthetic.ReducibilityFacts.

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.