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}.

(* TODO: move this to TheoryOfSeparationAxioms. *)
Theorem GC_Ext_Classical_collapse
{sepcon_orp_AX: SepconOrAxiomatization L Gamma}
{cpGamma: ClassicalPropositionalLogic L Gamma}
{gcsGamma: GarbageCollectSeparationLogic L Gamma}
{ExtsGamma: ExtSeparationLogic L Gamma}:
forall (x y: expr), |-- x * y <--> x && y.