End AdjointTheorems.
Section MonoTheorems.
Context {Mono: Monotonicity L Gamma prodp}.

(* Specifications: *)
Lemma prodp_iffp: forall x1 x2 y1 y2,
|-- x1 <--> x2 ->
|-- y1 <--> y2 ->
|-- prodp x1 y1 <--> prodp x2 y2.
Lemma fold_left_iffp: forall x1 x2 xs1 xs2,
(Forall2 (fun x1 x2 => |-- x1 <--> x2) xs1 xs2) ->
|-- x1 <--> x2 ->
|-- fold_left prodp xs1 x1 <--> fold_left prodp xs2 x2.