Section Lindenbaum_Trivial.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{GammaP: Provable L}
{GammaD: Derivable L}
{SC: NormalSequentCalculus L GammaP GammaD}
{bSC: BasicSequentCalculus L GammaD}
{fwSC: FiniteWitnessedSequentCalculus L GammaD}
{minSC: MinimumSequentCalculus L GammaD}
{ipSC: IntuitionisticPropositionalSequentCalculus L GammaD}
{cpSC: ClassicalPropositionalSequentCalculus L GammaD}
{minAX: MinimumAxiomatization L GammaP}
{ipAX: IntuitionisticPropositionalLogic L GammaP}.

Lemma Lindenbaum_cannot_derive_ensures_max_consistent
{AX: NormalAxiomatization L GammaP GammaD}:
forall x, Lindenbaum_ensures (cannot_derive x) (maximal consistent).