Section FSAT_PROP_ONLY_DEC.
Variable (Σ : fo_signature)
(H1 : discrete (rels Σ))
(H2 : forall r, ar_rels Σ r = 0)
(A : fol_form Σ).
End FSAT_PROP_ONLY_DEC.
(* Check FSAT_PROP_ONLY_DEC. Print Assumptions FSAT_PROP_ONLY_DEC. *)

Theorem FULL_MONADIC (Σ : fo_signature) :
{ _ : discrete (syms Σ) &
{ _ : discrete (rels Σ)
| (forall s, ar_syms Σ s <= 1)
/\ (forall r, ar_rels Σ r <= 1) } }
+ { _ : discrete (rels Σ)
| forall r, ar_rels Σ r = 0 }
-> forall A, decidable (FSAT Σ A).