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theorem proved term proof

energy_storage_density_hierarchy

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formal statement (Lean)

 177theorem energy_storage_density_hierarchy :
 178    phi_rung_energy (-10) < phi_rung_energy 0 ∧
 179    phi_rung_energy 0 < phi_rung_energy 45 := by

proof body

Term-mode proof.

 180  constructor
 181  · unfold phi_rung_energy
 182    apply mul_lt_mul_of_pos_left _ E_coh_storage_pos
 183    exact zpow_lt_zpow_right₀ one_lt_phi (by norm_num)
 184  · unfold phi_rung_energy
 185    apply mul_lt_mul_of_pos_left _ E_coh_storage_pos
 186    exact zpow_lt_zpow_right₀ one_lt_phi (by norm_num)
 187
 188/-! ## §V. Maximum Theoretical Density -/
 189
 190/-- The φ-ladder energy is strictly increasing: higher rungs always give more energy. -/

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