Section FromSepconWeakIffToSepconWeak.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{sepconL: SepconLanguage L}
{Gamma: Provable L}
{minAX: MinimumAxiomatization L Gamma}
{ipAX: IntuitionisticPropositionalLogic L Gamma}
{sepconAX: SepconAxiomatization_weak_iffp L Gamma}.

Lemma SepconAxiomatizationWeakIff2SepconAxiomatizationWeak:
SepconAxiomatization_weak L Gamma.