Section FSAT_in_dec.
(* The main theorem here:  - Given a discrete FO signature Σ - Given a finite and discrete base type X  Having a Σ-model over that base type X is a decidable property *)
Variables (Σ : fo_signature) (HΣ1 : discrete (syms Σ)) (HΣ2 : discrete (rels Σ))
(X : Type) (HX1 : finite_t X) (HX2 : discrete X)
(A : fol_form Σ).

Theorem FSAT_in_dec : decidable (@fo_form_fin_dec_SAT_in Σ A X).