Lemma MakeSequentCalculus_GodelDummettPropositionalLogic {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) {ipGamma': IntuitionisticPropositionalLogic L (Build_AxiomaticProofTheory (@provable L Gamma))} {gdpGamma: GodelDummettPropositionalLogic L Gamma}: Typeclass_Rewrite (exist (fun X: Prop => X) (IntuitionisticPropositionalLogic L (Build_AxiomaticProofTheory (@provable L Gamma))) ipGamma' :: nil) -> forall (G: Prop) (l: list (sig (fun X: Prop => X))), (forall (gdpGamma: GodelDummettPropositionalLogic L (Build_AxiomaticProofTheory (@provable L Gamma))), OpaqueProp (Typeclass_Rewrite l -> G)) <-> OpaqueProp (Typeclass_Rewrite ((exist (fun X: Prop => X) (GodelDummettPropositionalLogic L Gamma) gdpGamma) :: l) -> G).