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Minimality and contrasting examples for Schur order

theorem ProbabilityTheory.Copula.schurLE_independence_iff (C : Copula 2) : C.SchurLE (independence 2) ↔ C = independence 2

The least Schur equivalence class contains only independence.

theorem ProbabilityTheory.Copula.schurLE_not_antisymmetric : ¬∀ (C D : Copula 2), C.SchurLE D → D.SchurLE C → C = D

theorem ProbabilityTheory.Copula.not_schurLE_countermonotonic_independence : ¬countermonotonic.SchurLE (independence 2)

Concordance comparison does not imply Schur comparison.

theorem ProbabilityTheory.Copula.not_lowerOrthantLE_comonotonic_countermonotonic : ¬(comonotonic 2).LowerOrthantLE countermonotonic

Schur comparison does not imply concordance comparison.