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

Lemma assoc_prodp_fold_left_equiv: forall xs1 xs2,
|-- prodp (fold_left prodp xs1 e) (fold_left prodp xs2 e) <--> fold_left prodp (xs1 ++ xs2) e.