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

Lemma Σ2_Σn_soundness :
fo_form_fin_dec_SAT A
-> fo_form_fin_dec_SAT (Σ2_Σn A).