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theorem proved tactic proof

intensityAtRung_succ_ratio

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formal statement (Lean)

  46theorem intensityAtRung_succ_ratio (k : ℕ) :
  47    intensityAtRung (k + 1) = intensityAtRung k * phi⁻¹ := by

proof body

Tactic-mode proof.

  48  unfold intensityAtRung
  49  have hphi_ne : phi ≠ 0 := Constants.phi_ne_zero
  50  have hzpow : phi ^ (-((k : ℤ) + 1)) = phi ^ (-(k : ℤ)) * phi⁻¹ := by
  51    rw [show (-((k : ℤ) + 1)) = -(k : ℤ) + (-1 : ℤ) by ring]
  52    rw [zpow_add₀ hphi_ne]
  53    simp
  54  have hcast : ((k + 1 : ℕ) : ℤ) = (k : ℤ) + 1 := by push_cast; ring
  55  rw [hcast, hzpow]; ring
  56

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