theorem
proved
term proof
k_peak_adjacent_ratio
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formal statement (Lean)
48theorem k_peak_adjacent_ratio (k_0 : ℝ) (n : ℕ) (h : 0 < k_0) :
49 k_peak k_0 (n + 1) / k_peak k_0 n = phi := by
proof body
Term-mode proof.
50 unfold k_peak
51 have h_phi_ne : phi ≠ 0 := ne_of_gt phi_pos
52 have h_k0_ne : k_0 ≠ 0 := ne_of_gt h
53 have h_pow_n_ne : phi ^ n ≠ 0 := pow_ne_zero n h_phi_ne
54 rw [pow_succ]
55 field_simp
56
57/-- The second-to-first peak ratio is `φ`. -/