theorem healthy_eq_zero_profit {R c_min : ℝ}
(_hc : 0 < c_min) (hR : c_min < R) :
producerProfit R (healthyEquilibrium R c_min) c_min = 0 := by
unfold producerProfit healthyEquilibrium
rw [div_div_cancel₀ (ne_of_gt (by linarith : 0 < R))]; ringPaper 10: The Knowledge Commons Paradox: