End AdjointTheorems.
Section MonoTheorems.
Context {L: Language}
{minL: MinimunLanguage L}
{Gamma: ProofTheory L}
{minAX: MinimunAxiomatization L Gamma}
{prodp: expr -> expr -> expr}
{Mono: Monotonicity L Gamma prodp}.

Lemma fold_right_mono: forall x1 x2 xs1 xs2,
(Forall2 (fun x1 x2 => |-- x1 --> x2) xs1 xs2) ->
|-- x1 --> x2 ->
|-- fold_right prodp x1 xs1 --> fold_right prodp x2 xs2.