Section completeness.
Variables (X : Type)
(Mn : fo_model Σn X)
(H1 : finite_t X)
(H2 : fo_model_dec Mn)
(phi : nat -> X)
(H3 : fol_sem Mn phi (Σ2_Σn A)).
Let M2 : fo_model Σ2 X.
End completeness.

Lemma Σ2_Σn_completeness :
fo_form_fin_dec_SAT (Σ2_Σn A)
-> fo_form_fin_dec_SAT A.