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

Lemma andp_Comm: Commutativity L Gamma andp.