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_impp_iff: forall (Phi: context),
maximal consistent Phi ->
(forall x y: expr, Phi (x --> y) <-> (Phi x -> Phi y)).