theorem gini_nonneg (hJ : 0 < J) (s : Fin J → ℝ) :
0 ≤ giniIndex J s := by
simp only [giniIndex]
apply mul_nonneg
· apply div_nonneg one_pos.le
exact mul_nonneg (by norm_num) (by exact_mod_cast le_of_lt hJ)
· apply Finset.sum_nonneg; intro i _
apply Finset.sum_nonneg; intro j _
exact abs_nonneg _## CES Inequality Measures