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}.

Lemma core_tr_andp: forall x y, |-- core_tr (x && y) <--> core_tr x && core_tr y.