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theorem proved term proof

spectral_gap_pos_rung

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formal statement (Lean)

 178theorem spectral_gap_pos_rung {n : ℤ} (hn : 1 ≤ n) :
 179    Jcost phi ≤ Jcost (PhiLadder n) :=

proof body

Term-mode proof.

 180  Jcost_mono_gt_one (phiLadder_gt_one hn) one_lt_phi (phiLadder_ge_phi hn)
 181
 182/-- **The spectral gap theorem**: For all n ≠ 0, J(φⁿ) ≥ J(φ) > 0.
 183    Every non-vacuum φ-ladder configuration has cost at least Δ. -/

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