theorem more_heirs_lower_herfindahl {N₁ N₂ : ℕ} (hN₁ : 0 < N₁) (h : N₁ < N₂) :
bequestHerfindahl N₂ < bequestHerfindahl N₁ := by
simp only [bequestHerfindahl]
apply div_lt_div_of_pos_left one_pos
· exact Nat.cast_pos.mpr hN₁
· exact_mod_cast hFair Inheritance: Taxing Concentration, Not Transfer