log_2_in_interval

proof body

Tactic-mode proof.

 340  simp only [contains, log2Interval]
 341  constructor
 342  · -- 0.693 ≤ log 2
 343    have h := Real.log_two_gt_d9  -- 0.6931471803 < log 2
 344    have h1 : ((693 / 1000 : ℚ) : ℝ) < log 2 := by
 345      calc ((693 / 1000 : ℚ) : ℝ) = (0.693 : ℝ) := by norm_num
 346        _ < (0.6931471803 : ℝ) := by norm_num
 347        _ < log 2 := h
 348    exact le_of_lt h1
 349  · -- log 2 ≤ 0.694
 350    have h := Real.log_two_lt_d9  -- log 2 < 0.6931471808
 351    have h1 : log 2 < ((694 / 1000 : ℚ) : ℝ) := by
 352      calc log 2 < (0.6931471808 : ℝ) := h
 353        _ < (0.694 : ℝ) := by norm_num
 354        _ = ((694 / 1000 : ℚ) : ℝ) := by norm_num
 355    exact le_of_lt h1
 356
 357/-- Interval containing log(10) ≈ 2.3025 -/