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theorem Verification.maxProduct_independence_isSI (C : ProbabilityTheory.Copula 2) (hC : C.IsSI) (α β : ↑unitInterval) : (C.maxProduct (ProbabilityTheory.Copula.independence 2) ![α, β]).IsSI

theorem Verification.maxProduct_independence_transpose (C : ProbabilityTheory.Copula 2) (α β : ↑unitInterval) : (C.maxProduct (ProbabilityTheory.Copula.independence 2) ![α, β]).transpose = C.transpose.maxProduct (ProbabilityTheory.Copula.independence 2) ![β, α]

theorem Verification.maxProduct_independence_isCI (C : ProbabilityTheory.Copula 2) (hC : C.IsCI) (α β : ↑unitInterval) : (C.maxProduct (ProbabilityTheory.Copula.independence 2) ![α, β]).IsCI