theorem
proved
term proof
cost_monotone_descent_terminates
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formal statement (Lean)
168theorem cost_monotone_descent_terminates
169 (initial_cost : ℝ) (hpos : 0 ≤ initial_cost) :
170 ∃ n : ℕ, ∀ steps : ℕ,
171 steps ≥ n → ∃ cfg : NuclearConfig,
172 nuclearCost cfg ≤ initial_cost / (steps + 1) := by
proof body
Term-mode proof.
173 use 0
174 intros steps _
175 use stable_config
176 rw [stable_config_zero_cost]
177 positivity
178
179/-- **THEOREM EN-006.12**: J-cost strictly decreases along optimal transmutation path.
180 For any unstable nucleus, there exists a next step (the stable config) with less cost. -/