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theorem proved tactic proof

phi_lt_two

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formal statement (Lean)

  52theorem phi_lt_two : phi < 2 := by

proof body

Tactic-mode proof.

  53  unfold phi
  54  have h5 : Real.sqrt 5 < 3 := by
  55    rw [show (3 : ℝ) = Real.sqrt 9 from by rw [show (9:ℝ) = 3^2 from by norm_num, Real.sqrt_sq (by norm_num : (3:ℝ) ≥ 0)]]
  56    exact Real.sqrt_lt_sqrt (by norm_num) (by norm_num)
  57  linarith
  58
  59/-- Each phi-bit carries more information than a Shannon bit because
  60    phi < 2: fewer phi-bits are needed to encode the same number of states. -/

used by (23)

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depends on (10)

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