End DerivableRulesFromSequentCalculus2.
Section DerivableRulesFromAxiomatization2.
Context {L: Language}
{minL: MinimunLanguage L}
{pL: PropositionalLanguage L}
{Gamma: ProofTheory L}
{minAX: MinimunAxiomatization L Gamma}
{ipGamma: IntuitionisticPropositionalLogic L Gamma}.

Lemma demorgan_orp_negp: forall (x y: expr),
|-- ~~ x || ~~ y --> ~~ (x && y).