theorem two_period_overinvestment {V c : ℝ} {N : ℕ}
(hV : 0 < V) (_hc : 0 < c) (_hN : 2 ≤ N) :
c / ↑N < V / ↑N → c / ↑N < V := by
intro h
have hN_ge1 : (1 : ℝ) ≤ ↑N := by exact_mod_cast (by omega : 1 ≤ N)
calc c / ↑N < V / ↑N := h
_ ≤ V := div_le_self (le_of_lt hV) hN_ge1Paper 6: Endogenous Decentralization and the AI Transition