Section DeMorgan.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{Gamma: Provable L}
{minAX: MinimumAxiomatization L Gamma}
{ipAX: IntuitionisticPropositionalLogic L Gamma}
{dmpAX: DeMorganPropositionalLogic L Gamma}.

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