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theorem proved term proof

phi_rung_energy_ratio

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formal statement (Lean)

  71theorem phi_rung_energy_ratio (n : ℤ) :
  72    phi_rung_energy (n + 1) / phi_rung_energy n = phi := by

proof body

Term-mode proof.

  73  unfold phi_rung_energy
  74  rw [zpow_add_one₀ phi_ne_zero]
  75  have hpow_pos : 0 < phi ^ n := zpow_pos phi_pos n
  76  field_simp [phi_pos.ne', E_coh_storage_pos.ne', hpow_pos.ne']
  77
  78/-! ## §II. Energy Hierarchy -/
  79
  80/-- Chemical bonding rung index (n = 0, one coherence quantum). -/

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