Section AdjointTheorems.
Context {L: Language}
{minL: MinimumLanguage L}
{Gamma: Provable L}
{minAX: MinimumAxiomatization L Gamma}
{prodp funcp: expr -> expr -> expr}
{Adj: Adjointness L Gamma prodp funcp}.

Lemma prodp_mono1: forall x1 x2 y, |-- x1 --> x2 -> |-- prodp x1 y --> prodp x2 y.