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theorem proved term proof

restoring_force_negative

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formal statement (Lean)

 277theorem restoring_force_negative (σ : ℝ) (hσ : σ < 0) :
 278    deriv extractionSystemCost σ < 0 := by

proof body

Term-mode proof.

 279  rw [deriv_extraction_cost]
 280  have : Real.sinh σ < Real.sinh 0 := Real.sinh_strictMono hσ
 281  simp only [Real.sinh_zero] at this; linarith
 282
 283/-- **Theorem (Universal Restoring Force)**: For any σ ≠ 0, the product
 284    σ · C'(σ) > 0, meaning the cost gradient always opposes the extraction.
 285    The universe structurally resists imbalance. -/

depends on (5)

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