Section ModalLogic.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{mL: ModalLanguage L}
{Gamma: Provable L}
{AX: NormalAxiomatization L Gamma}
{minAX: MinimumAxiomatization L Gamma}
{ipGamma: IntuitionisticPropositionalLogic L Gamma}
{KmGamma: SystemK L Gamma}.

Lemma deduction_axiom_K: forall Phi x y,
Phi |-- boxp (x --> y) ->
Phi |-- boxp x --> boxp y.