Local Open Scope logic_base.
Local Open Scope syntax.
Section DerivedRules.
Context {L: Language}
{minL: MinimunLanguage L}
{pL: PropositionalLanguage L}
{sL: SeparationLanguage L}
{Gamma: ProofTheory L}
{minAX: MinimunAxiomatization L Gamma}
{ipGamma: IntuitionisticPropositionalLogic L Gamma}
{sGamma: SeparationLogic L Gamma}.

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