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}.

Theorem GC_Ext_Classical_collapse {cpGamma: ClassicalPropositionalLogic L Gamma} {gcsGamma: GarbageCollectSeparationLogic L Gamma} {ExtsGamma: ExtSeparationLogic L Gamma}: forall (x y: expr),
|-- x * y <--> x && y.