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

Lemma assoc_fold_left_Permutation: forall x ys1 ys2,
Permutation ys1 ys2 ->
|-- fold_left prodp ys1 x <--> fold_left prodp ys2 x.