Section CoreTransit.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{sepconL: SepconLanguage L}
{wandL: WandLanguage L}
{CtsL: CoreTransitSeparationLanguage L}
{Gamma: Provable L}
{minAX: MinimumAxiomatization L Gamma}
{ipAX: IntuitionisticPropositionalLogic L Gamma}
{sepconAX: SepconAxiomatization L Gamma}
{CosAX: Corable L Gamma}
{CtsGamma: CoreTransitSeparationLogic L Gamma}.
Instance core_tr_proper_impp: Proper ((fun x y => |-- impp x y) ==> (fun x y => |-- impp x y)) core_tr.

Lemma core_tr_dup {GC: GarbageCollectSeparationLogic L Gamma}: forall x, |-- core_tr x <--> core_tr x * core_tr x.