End DerivableRulesFromSequentCalculus2.
Section DerivableRulesFromAxiomatization2.
Context {L: Language}
{minL: MinimunLanguage L}
{pL: PropositionalLanguage L}
{Gamma: ProofTheory L}
{minAX: MinimunAxiomatization L Gamma}
{ipGamma: IntuitionisticPropositionalLogic L Gamma}.

Lemma orp_assoc: forall (x y z: expr),
|-- x || y || z <--> x || (y || z).