Hint Rewrite <- @MakeAxiomatization_IntuitionisticPropositionalSequentCalculus using first [typeclasses eauto | instantiate_must_succeed; apply Typeclass_Rewrite_I]: AddAX.
Section Axiomatization2SequentCalculus.

(* Specifications: *)
Lemma Axiomatization2SequentCalculus_ipSC {L: Language} {minL: MinimunLanguage L} {pL: PropositionalLanguage L} {Gamma: ProofTheory L} {AX: NormalAxiomatization L Gamma} {minAX: MinimunAxiomatization L Gamma} {ipGamma: IntuitionisticPropositionalLogic L Gamma}: IntuitionisticPropositionalSequentCalculus L Gamma.
End Axiomatization2SequentCalculus.
Lemma MakeSequentCalculus_IntuitionisticPropositionalLogic {L: Language} {minL: MinimunLanguage L} {pL: PropositionalLanguage L} {Gamma: ProofTheory L} {minAX: MinimunAxiomatization L Gamma} (minAX': MinimunAxiomatization L (Build_AxiomaticProofTheory (@provable L Gamma))) (ipGamma: IntuitionisticPropositionalLogic L Gamma):
Typeclass_Rewrite ((exist (fun X: Prop => X) (MinimunAxiomatization L (Build_AxiomaticProofTheory (@provable L Gamma))) minAX') :: nil) ->
forall (G: Prop) (l: list (sig (fun X: Prop => X))),
(forall
(ipSC: IntuitionisticPropositionalSequentCalculus L (Build_AxiomaticProofTheory (@provable L Gamma)))
(ipGamma: IntuitionisticPropositionalLogic L (Build_AxiomaticProofTheory (@provable L Gamma))),
OpaqueProp (OpaqueProp (Typeclass_Rewrite l -> G))) <->
OpaqueProp (Typeclass_Rewrite ((exist (fun X: Prop => X) (IntuitionisticPropositionalLogic L Gamma) ipGamma) :: l) -> G).