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theorem proved term proof

phi_ladder_energy_strictly_increasing

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formal statement (Lean)

 191theorem phi_ladder_energy_strictly_increasing (n m : ℤ) (h : n < m) :
 192    phi_rung_energy n < phi_rung_energy m := by

proof body

Term-mode proof.

 193  unfold phi_rung_energy
 194  apply mul_lt_mul_of_pos_left _ E_coh_storage_pos
 195  exact zpow_lt_zpow_right₀ one_lt_phi h
 196
 197/-! ## §VI. Fundamental Bound Summary -/
 198
 199/-- The RS energy storage hierarchy theorem.
 200    Derives three distinct energy scales from the φ-ladder structure. -/

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