Local Open Scope logic_base.
Local Open Scope syntax.
Section Lindenbaum_Flat.
Context {L: Language}
{minL: MinimunLanguage L}
{pL: PropositionalLanguage L}
{sL: SeparationLanguage L}
{Gamma: ProofTheory L}
{SC: NormalSequentCalculus L Gamma}
{bSC: BasicSequentCalculus L Gamma}
{fwSC: FiniteWitnessedSequentCalculus L Gamma}
{minSC: MinimunSequentCalculus L Gamma}
{ipSC: IntuitionisticPropositionalSequentCalculus L Gamma}
{AX: NormalAxiomatization L Gamma}
{minAX: MinimunAxiomatization L Gamma}
{ipGamma: IntuitionisticPropositionalLogic L Gamma}
{sGamma: SeparationLogic L Gamma}.

Lemma Lindenbaum_context_sepcon_included_l_ensures_consistent: forall Phi Psi
(CONSI: consistent Psi),
Lindenbaum_ensures (context_sepcon_included_l Phi Psi) consistent.