End DerivableRulesFromSequentCalculus1.
Section SequentCalculus2Axiomatization.
Context {L: Language}
{minL: MinimunLanguage L}
{pL: PropositionalLanguage L}
{Gamma: ProofTheory L}
{SC: NormalSequentCalculus L Gamma}
{bSC: BasicSequentCalculus L Gamma}
{minSC: MinimunSequentCalculus L Gamma}
{ipSC: IntuitionisticPropositionalSequentCalculus L Gamma}
{minAX: MinimunAxiomatization L Gamma}.

Lemma MakeAxiomatization_IntuitionisticPropositionalSequentCalculus {L: Language} {minL: MinimunLanguage L} {pL: PropositionalLanguage L} {Gamma: ProofTheory L} {bSC: BasicSequentCalculus L Gamma} {minSC: MinimunSequentCalculus L Gamma} {minAX': MinimunAxiomatization L (Build_SequentCalculus (@derivable L Gamma))} (ipSC: IntuitionisticPropositionalSequentCalculus L Gamma):
Typeclass_Rewrite ((exist (fun X: Prop => X) (MinimunAxiomatization L (Build_SequentCalculus (@derivable L Gamma))) minAX') :: nil) ->
forall (G: Prop) (l: list (sig (fun X: Prop => X))),
(forall
(ipSC: IntuitionisticPropositionalSequentCalculus L (Build_SequentCalculus (@derivable L Gamma)))
(ipGamma: IntuitionisticPropositionalLogic L (Build_SequentCalculus (@derivable L Gamma))),
OpaqueProp (OpaqueProp (Typeclass_Rewrite l -> G))) <->
OpaqueProp (Typeclass_Rewrite ((exist (fun X: Prop => X) (IntuitionisticPropositionalSequentCalculus L Gamma) ipSC) :: l) -> G).