Definition multi_imp {L: Language} {minL: MinimunLanguage L} (xs: list expr) (y: expr): expr :=
  fold_right impp y xs.Class NormalAxiomatization (L: Language) {minL: MinimunLanguage L} (Gamma: ProofTheory L): Type := {
  derivable_provable: forall Phi y, derivable Phi y <->
                        exists xs, Forall (fun x => Phi x) xs /\ provable (multi_imp xs y)
}.Class NormalAxiomatization (L: Language) {minL: MinimunLanguage L} (Gamma: ProofTheory L): Type := {
  derivable_provable: forall Phi y, derivable Phi y <->
                        exists xs, Forall (fun x => Phi x) xs /\ provable (multi_imp xs y)
}.

Theorem SequentCalculus2Axiomatization_AX {fwSC: FiniteWitnessedSequentCalculus L Gamma}: NormalAxiomatization L Gamma.