End MonoTheorems.
Section AssocTheorems.
Context {e: expr}
{Mono: Monotonicity L Gamma prodp}
{Assoc: Associativity L Gamma prodp}.

Lemma prodp_assoc: forall x y z, |-- prodp x (prodp y z) <--> prodp (prodp x y) z.
Context {LU: LeftUnit L Gamma e prodp}
{RU: RightUnit L Gamma e prodp}.