Section DerivableRules.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{Gamma: Provable L}
{minAX: MinimumAxiomatization L Gamma}
{ipAX: IntuitionisticPropositionalLogic L Gamma}.
Definition multi_and (xs: list expr): expr := fold_left andp xs truep.

Lemma multi_and_multi_imp: forall (xs: list expr) (y: expr),
|-- (multi_and xs --> y) <--> (multi_imp xs y).