Local Open Scope logic_base.
Local Open Scope syntax.
Section ContextProperties.
Context {L: Language}
{minL: MinimunLanguage L}
{pL: PropositionalLanguage L}
{Gamma: ProofTheory L}
{bSC: BasicSequentCalculus L Gamma}
{minSC: MinimunSequentCalculus L Gamma}
{ipSC: IntuitionisticPropositionalSequentCalculus L Gamma}
{cpSC: ClassicalPropositionalSequentCalculus L Gamma}.

Lemma DDCS_MCS: forall (Phi: context),
derivable_closed Phi ->
orp_witnessed Phi ->
consistent Phi ->
maximal consistent Phi.