Hint Rewrite <- @MakeSequentCalculus_DeMorganPropositionalLogic using (instantiate (1 := _); apply Typeclass_Rewrite_I): AddSC.
Section ModalLogic.
Context {L: Language}
{minL: MinimunLanguage L}
{pL: PropositionalLanguage L}
{mL: ModalLanguage L}
{Gamma: ProofTheory L}
{AX: NormalAxiomatization L Gamma}
{minAX: MinimunAxiomatization L Gamma}
{ipGamma: IntuitionisticPropositionalLogic L Gamma}
{KmGamma: SystemK L Gamma}.

(* Specifications: *)
Lemma derivable_axiom_K: forall Phi x y,
Phi |-- boxp (x --> y) --> (boxp x --> boxp y).
Lemma deduction_axiom_K: forall Phi x y,
Phi |-- boxp (x --> y) ->
Phi |-- boxp x --> boxp y.
Lemma derivable_axiom_T {TmGamma: SystemT L Gamma}: forall Phi x ,
Phi |-- boxp x --> x.
Lemma deduction_axiom_T {TmGamma: SystemT L Gamma}: forall Phi x ,
Phi |-- boxp x ->
Phi |-- x.