Definition In_freeVarSys (v : nat) (T : fol.System L) :=
  exists f : fol.Formula L, In v (freeVarFormula f) /\ mem _ T f.

(* Specifications: *)
Lemma notInFreeVarSys : forall x, ~ In_freeVarSys x (Ensembles.Empty_set (fol.Formula L)).