Local Open Scope logic_base.
Local Open Scope kripke_model.
Section Lindenbaum_Kripke.
Context {L: Language}
{minL: MinimunLanguage L}
{Gamma: ProofTheory L}
{bSC: BasicSequentCalculus L Gamma}
{fwSC: FiniteWitnessedSequentCalculus L Gamma}.

(* Specifications: *)
Lemma Lindenbaum_preserves_cannot_derive: forall x, Lindenbaum_preserves (cannot_derive x).
Lemma Lindenbaum_cannot_derive_ensures_derivable_closed: forall x, Lindenbaum_ensures (cannot_derive x) derivable_closed.
End Lindenbaum_Kripke.