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lemma proved term proof

log2_half

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formal statement (Lean)

  45lemma log2_half : log2 (1/2 : ℝ) = -1 := by

proof body

Term-mode proof.

  46  unfold log2
  47  simp only [one_div]
  48  rw [Real.logb_inv 2 2]
  49  rw [Real.logb_self_eq_one (by norm_num : (1 : ℝ) < 2)]
  50
  51/-! ## Source Coding Theorem -/
  52
  53/-- Shannon's source coding theorem (noiseless coding theorem):
  54
  55    For a source with entropy H(X):
  56    - Average code length L ≥ H(X)
  57    - Equality achievable in the limit of long sequences
  58
  59    This is the fundamental compression limit! -/

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