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

Lemma prodp_iffp: forall x1 x2 y1 y2,
|-- x1 <--> x2 ->
|-- y1 <--> y2 ->
|-- prodp x1 y1 <--> prodp x2 y2.