Section FromEmpIffToEmp.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{sepconL: SepconLanguage L}
{empL: EmpLanguage L}
{Gamma: Provable L}
{minAX: MinimumAxiomatization L Gamma}
{ipAX: IntuitionisticPropositionalLogic L Gamma}
{sepconAX: SepconAxiomatization L Gamma}
{empAX: EmpAxiomatization_iffp L Gamma}.

Lemma EmpAxiomatizationIff2EmpAxiomatization:
EmpAxiomatization L Gamma.