Section DerivableRulesFromSequentCalculus1.
Context {L: Language}
{minL: MinimumLanguage L}
{pL: PropositionalLanguage L}
{Gamma: Derivable L}
{bSC: BasicSequentCalculus L Gamma}
{minSC: MinimumSequentCalculus L Gamma}
{ipSC: IntuitionisticPropositionalSequentCalculus L Gamma}.

Lemma deduction_contradiction_elim: forall (Phi: context) (x y: expr),
Phi |-- x ->
Phi |-- ~~ x ->
Phi |-- y.