Section DerivableRulesFromPatterns.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{Gamma: Provable L}
{minAX: MinimumAxiomatization L Gamma}
{ipAX: IntuitionisticPropositionalLogic L Gamma}
{prodp: expr -> expr -> expr}.

Lemma prodp_comm {Comm: Commutativity L Gamma prodp}: forall x y,
|-- prodp x y <--> prodp y x.