Section CommForSimpleAssocConstruction.
Context {L: Language}
{minL: MinimumLanguage L}
{Gamma: Provable L}
{minAX: MinimumAxiomatization L Gamma}
{prodp: expr -> expr -> expr}
{Comm: Commutativity L Gamma prodp}
{Mono: Monotonicity L Gamma prodp}.

Lemma Build_Associativity1:
(forall x y z, |-- prodp x (prodp y z) --> prodp (prodp x y) z) ->
Associativity L Gamma prodp.