theorem baumol_bounded_below {beta_Z g_C g_Z : ℝ}
(_hbeta : 0 ≤ beta_Z) (_hbeta1 : beta_Z ≤ 1) (hgZ_le : g_Z ≤ g_C) :
g_Z ≤ baumolGrowthRate beta_Z g_C g_Z := by
unfold baumolGrowthRate; nlinarithPaper 6: Endogenous Decentralization and the AI Transition