End DerivableRulesFromAxiomatization1.
Section DerivableRulesFromSequentCalculus.
Context {L: Language}
{minL: MinimunLanguage L}
{pL: PropositionalLanguage L}
{Gamma: ProofTheory L}
{bSC: BasicSequentCalculus L Gamma}
{minSC: MinimunSequentCalculus L Gamma}
{ipSC: IntuitionisticPropositionalSequentCalculus L Gamma}
{cpSC: ClassicalPropositionalSequentCalculus L Gamma}.

(* Specifications: *)
Lemma deduction_contrapositiveNN: forall Phi (x y: expr),
Phi |-- ~~ y --> ~~ x ->
Phi |-- x --> y.
Lemma deduction_contrapositiveNP: forall Phi (x y: expr),
Phi |-- ~~ y --> x ->
Phi |-- ~~ x --> y.