Require Export Coq.Lists.List.
Local Open Scope logic_base.
Section Lindenbaum.
Context {L: Language}
{Gamma: ProofTheory L}
{bSC: BasicSequentCalculus L Gamma}.

Lemma Lindenbaum_for_derivable_closed: forall P,
Lindenbaum_preserves P ->
derivable_subset_preserved P ->
Lindenbaum_ensures P derivable_closed.