Section AddAxiomatization.
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}
{minAX: MinimunAxiomatization L (Build_SequentCalculus (@derivable L Gamma))}
{ipGamma: IntuitionisticPropositionalLogic L (Build_SequentCalculus (@derivable L Gamma))}
{SC': NormalSequentCalculus L (Build_SequentCalculus (@derivable L Gamma))}
{bSC': BasicSequentCalculus L (Build_SequentCalculus (@derivable L Gamma))}
{minSC': MinimunSequentCalculus L (Build_SequentCalculus (@derivable L Gamma))}
{ipSC': IntuitionisticPropositionalSequentCalculus L (Build_SequentCalculus (@derivable L Gamma))}.

Lemma MakeAxiomatization_ClassicalPropositionalSequentCalculus:
Typeclass_Rewrite (exist (fun X: Prop => X) (IntuitionisticPropositionalLogic L (Build_SequentCalculus (@derivable L Gamma))) ipGamma :: exist (fun X: Prop => X) (IntuitionisticPropositionalSequentCalculus L (Build_SequentCalculus (@derivable L Gamma))) ipSC' :: exist (fun X: Prop => X) (BasicSequentCalculus L (Build_SequentCalculus (@derivable L Gamma))) bSC' :: exist (fun X: Prop => X) (MinimunSequentCalculus L (Build_SequentCalculus (@derivable L Gamma))) minSC' :: nil) ->
forall (G: Prop) (l: list (sig (fun X: Prop => X))),
(forall
(cpSC: ClassicalPropositionalSequentCalculus L (Build_SequentCalculus (@derivable L Gamma)))
(cpGamma: ClassicalPropositionalLogic L (Build_SequentCalculus (@derivable L Gamma))),
OpaqueProp (Typeclass_Rewrite l -> G)) <->
OpaqueProp (Typeclass_Rewrite ((exist (fun X: Prop => X) (ClassicalPropositionalSequentCalculus L Gamma) cpSC) :: l) -> G).