Hint Rewrite <- @MakeSequentCalculus_DeMorganPropositionalLogic using (instantiate (1 := _); apply Typeclass_Rewrite_I): AddSC.
Section DeMorgan.
Context {L: Language}
{minL: MinimunLanguage L}
{pL: PropositionalLanguage L}
{Gamma: ProofTheory L}
{minAX: MinimunAxiomatization L Gamma}
{ipGamma: IntuitionisticPropositionalLogic L Gamma}
{dmpGamma: DeMorganPropositionalLogic L Gamma}.

(* Lemma derivable_weak_excluded_middle: forall (Phi: context) (x: expr), Phi |-- ~~ x || ~~ ~~ x. *)
Lemma demorgan_negp_andp: forall (x y: expr),
|-- ~~ (x && y) <--> (~~ x || ~~ y).