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_left_mono2: forall x1 x2 xs,
|-- x1 --> x2 ->
|-- fold_left prodp xs x1 --> fold_left prodp xs x2.