Section FSAT_FULL_MONADIC_DEC.
(* I do not think we can be more general than that. In particular, decidability of FSAT implies discreteness I think. For instance, let r1 and r2 be two rels then ~ (r1(£0,..,£k) <-> r2(£0,..,£k)) is satisfiable iff r1 <> r2 ?? TO CHECK *)
Variable (Σ : fo_signature)
(H1 : discrete (syms Σ))
(H2 : discrete (rels Σ))
(H3 : forall s, ar_syms Σ s <= 1)
(H4 : forall r, ar_rels Σ r <= 1)
(A : fol_form Σ).

Theorem FSAT_FULL_MONADIC_DEC : decidable (FSAT _ A).