Section ContextProperties.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{Gamma: Derivable L}
{bSC: BasicSequentCalculus L Gamma}
{minSC: MinimumSequentCalculus L Gamma}
{ipSC: IntuitionisticPropositionalSequentCalculus L Gamma}
{cpSC: ClassicalPropositionalSequentCalculus L Gamma}.

Lemma MCS_nonelement_inconsistent: forall (Phi: context),
maximal consistent Phi ->
(forall x: expr, ~ Phi x <-> Phi |-- x --> FF).