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lemma proved term proof

phi5_mul_phi5

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formal statement (Lean)

 165private lemma phi5_mul_phi5 : phi ^ (5 : ℝ) * phi ^ (5 : ℝ) = phi ^ (10 : ℝ) := by

proof body

Term-mode proof.

 166  rw [← Real.rpow_add phi_pos]; norm_num
 167
 168/-- Fibonacci form of κ: κ = 8(5φ + 3).
 169
 170    Via φ⁵ = 5φ + 3 (Fibonacci identity: F₅=5, F₄=3, F₆=8):
 171    κ = F₆ · (F₅ · φ + F₄) = 8 · (5φ + 3). -/

depends on (7)

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