theorem trivial_fixed_point (lambda mu : ℝ) {cost : ℝ} (hcost : 0 ≤ cost) :
netEntryFlow lambda mu 0 cost 0 = 0 := by
simp only [netEntryFlow, entryRate, exitRate, mul_zero, sub_zero]
simp only [max_eq_left (show 0 - cost ≤ 0 by linarith), mul_zero]## Entry-Exit Dynamics