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theorem Papers.AnsariRockel2024.laplace_not_independent_zero : Verification.laplaceBivariate 0 ⋯ ≠ ProbabilityTheory.Copula.independence 2

theorem Papers.AnsariRockel2024.laplace_not_isPQD_nonpositive (r : ℝ) (hr : r ∈ Set.Icc (-1) 1) (hn : r ≤ 0) : ¬(Verification.laplaceBivariate r hr).IsPQD

theorem Papers.AnsariRockel2024.laplace_not_isNQD_nonnegative (r : ℝ) (hr : r ∈ Set.Icc (-1) 1) (hn : 0 ≤ r) : ¬(Verification.laplaceBivariate r hr).IsNQD

theorem Papers.AnsariRockel2024.laplace_not_isCI_nonpositive (r : ℝ) (hr : r ∈ Set.Icc (-1) 1) (hn : r ≤ 0) : ¬(Verification.laplaceBivariate r hr).IsCI

theorem Papers.AnsariRockel2024.laplace_not_isCD_nonnegative (r : ℝ) (hr : r ∈ Set.Icc (-1) 1) (hn : 0 ≤ r) : ¬(Verification.laplaceBivariate r hr).IsCD

theorem Papers.AnsariRockel2024.laplace_not_hasMTP2Density_nonpositive (r : ℝ) (hr : r ∈ Set.Icc (-1) 1) (hn : r ≤ 0) : ¬(Verification.laplaceBivariate r hr).HasMTP2Density

theorem Papers.AnsariRockel2024.laplace_not_hasMTP2Density (r : ℝ) (hr : r ∈ Set.Icc (-1) 1) : ¬(Verification.laplaceBivariate r hr).HasMTP2Density