Hint Rewrite <- @MakeAxiomatization_BasicSequentCalculus: AddAX.

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