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Exact Schur ordering of FGM copulas

Schur order compares absolute parameters. The proof averages a conditional CDF with its measure-preserving reflection and applies convexity.

theorem ProbabilityTheory.Copula.fgmConditionalCDF_le_one (θ : ℝ) (hθ : |θ| ≤ 1) (u v : ↑unitInterval) : fgmConditionalCDF θ u v ≤ 1

theorem ProbabilityTheory.Copula.schurLE_fgm_iff {θ η : ℝ} (hθ : |θ| ≤ 1) (hη : |η| ≤ 1) : (fgm θ hθ).SchurLE (fgm η hη) ↔ |θ| ≤ |η|

theorem ProbabilityTheory.Copula.schurBothLE_fgm_iff {θ η : ℝ} (hθ : |θ| ≤ 1) (hη : |η| ≤ 1) : (fgm θ hθ).SchurBothLE (fgm η hη) ↔ |θ| ≤ |η|