theorem logistic_fragility_negative {u : ℝ} (hu_gt : 1 / 2 < u) (hu_lt1 : u < 1) :
logisticElasticity u < 0 := by
simp only [logisticElasticity]
apply div_neg_of_neg_of_pos
· linarith
· linarithTheorems 7-8, Propositions 5 and 7, Corollary 3: