Section DerivedRules.
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 L Gamma}.

Lemma provable_sepcon_andp_left: forall (x y z: expr),
|-- (x && y) * z --> (x * z) && (y * z).