theorem bifurcation_condition {R c_min : ℝ} (hc : 0 < c_min) :
0 < healthyEquilibrium R c_min ↔ 0 < R := by
unfold healthyEquilibrium
constructor
· intro h
by_contra h'
push_neg at h'
linarith [div_nonpos_of_nonpos_of_nonneg h' hc.le]
· intro h
exact div_pos h hcPaper 10: The Knowledge Commons Paradox: