Section nested.
Variables (A : fol_form (Σrel n))
(X : Type) (Mn : fo_model (Σrel n) X)
(X_fin : finite_t X)
(X_discr : discrete X)
(Mn_dec : fo_model_dec Mn)
(φ : nat -> X)
(HA : fol_sem Mn φ A).
Let R := fom_rels Mn tt.
Local Lemma SATn_to_SAT2 : exists Y, fo_form_fin_dec_SAT_in (@Σn_Σ2_enc n A) Y.
End nested.

Theorem SATn_SAT2 A : fo_form_fin_discr_dec_SAT A
-> fo_form_fin_dec_SAT (@Σn_Σ2_enc n A).