Hint Rewrite <- @MakeAxiomatization_MinimunSequentCalculus using (typeclasses eauto): AddAX.

Lemma MakeAxiomatization_FiniteWitnessedSequentCalculus {L: Language} {minL: MinimunLanguage L} {Gamma: ProofTheory L} {fwSC: FiniteWitnessedSequentCalculus L Gamma} {bSC': BasicSequentCalculus L (Build_SequentCalculus (@derivable L Gamma))} {minSC': MinimunSequentCalculus L (Build_SequentCalculus (@derivable L Gamma))}:
forall (G: Prop) (l: list (sig (fun X: Prop => X))),
(forall
(fwSC: FiniteWitnessedSequentCalculus L (Build_SequentCalculus (@derivable L Gamma)))
(AX: NormalAxiomatization L (Build_SequentCalculus (@derivable L Gamma))),
OpaqueProp (OpaqueProp (Typeclass_Rewrite l -> G))) <->
OpaqueProp (Typeclass_Rewrite ((exist (fun X: Prop => X) (FiniteWitnessedSequentCalculus L Gamma) fwSC) :: l) -> G).