Section Lindenbaum_Flat.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{sepconL: SepconLanguage L}
{wandL: WandLanguage 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}
{AX: NormalAxiomatization L GammaP GammaD}
{minAX: MinimumAxiomatization L GammaP}
{ipAX: IntuitionisticPropositionalLogic L GammaP}
{sepconAX: SepconAxiomatization L GammaP}
{wandAX: WandAxiomatization L GammaP}
{sepcon_orp_AX: SepconOrAxiomatization L GammaP}
{sepcon_falsep_AX: SepconFalseAxiomatization L GammaP}.

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