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theorem proved tactic proof

syncPeriod_eq_mul

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formal statement (Lean)

  61theorem syncPeriod_eq_mul (D : ℕ) : syncPeriod D = (2 ^ D) * 45 := by

proof body

Tactic-mode proof.

  62  unfold syncPeriod
  63  have h2 : Nat.Coprime 2 45 := by decide
  64  have h : Nat.Coprime (2 ^ D) 45 := h2.pow_left D
  65  simpa using h.lcm_eq_mul
  66
  67/-! ### Synchronization Selection Principle (proved) -/
  68
  69/-- A direct formalization of the paper's minimization statement:
  70among all `D ≥ 3`, the function `D ↦ lcm(2^D,45)` is minimized uniquely at `D = 3`. -/

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