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theorem proved term proof

phi_ladder_unbounded

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formal statement (Lean)

  97theorem phi_ladder_unbounded (T : ℝ) (hT : 0 < T) :
  98    ∃ n : ℤ, T < T_c_rung n := by

proof body

Term-mode proof.

  99  unfold T_c_rung
 100  -- phi⁻¹ < 1 since phi > 1, so phi⁻¹^k → 0 as k → ∞
 101  -- equivalently phi^k → ∞
 102  obtain ⟨n, hn⟩ := pow_unbounded_of_one_lt T one_lt_phi
 103  exact ⟨(n : ℤ), by rw [zpow_natCast]; exact hn⟩
 104
 105/-! ## §III. Superconducting Gap -/
 106
 107/-- The superconducting gap function Δ in RS.
 108    Δ is proportional to E_coh reduced by the thermal competition ratio.
 109    When T < T_c, gap Δ > 0 (superconducting); when T ≥ T_c, Δ = 0 (normal). -/

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