Section DerivableRulesFromAxiomatization1.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{Gamma: Provable L}
{minAX: MinimumAxiomatization L Gamma}
{ipAX: IntuitionisticPropositionalLogic L Gamma}
{cpAX: ClassicalPropositionalLogic L Gamma}.
Instance Classical2GodelDummett: GodelDummettPropositionalLogic L Gamma.

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