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

(* Specifications: *)
Lemma impp_andp_Adjoint: Adjointness L Gamma andp impp.
Lemma andp_Comm: Commutativity L Gamma andp.
Lemma andp_Mono: Monotonicity L Gamma andp.
Lemma andp_LU: LeftUnit L Gamma TT andp.
Lemma andp_RU: RightUnit L Gamma TT andp.
Lemma andp_Assoc: Associativity L Gamma andp.
End PatternInstances.