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theorem proved tactic proof

e_in_eInterval

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formal statement (Lean)

  79theorem e_in_eInterval : eInterval.contains (exp 1) := by

proof body

Tactic-mode proof.

  80  simp only [Interval.contains, eInterval]
  81  constructor
  82  · -- 2.718 ≤ exp(1)
  83    have h := Real.exp_one_gt_d9  -- 2.7182818283 < exp 1
  84    have h1 : ((2718 / 1000 : ℚ) : ℝ) = (2.718 : ℝ) := by norm_num
  85    linarith
  86  · -- exp(1) ≤ 2.719
  87    have h := Real.exp_one_lt_d9  -- exp 1 < 2.7182818286
  88    have h1 : ((2719 / 1000 : ℚ) : ℝ) = (2.719 : ℝ) := by norm_num
  89    linarith
  90
  91end IndisputableMonolith.Numerics

depends on (5)

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