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theorem proved tactic proof

pi_pow5_in_interval_tight

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formal statement (Lean)

 245theorem pi_pow5_in_interval_tight : piPow5IntervalTight.contains (pi ^ 5) := by

proof body

Tactic-mode proof.

 246  simp only [contains, piPow5IntervalTight]
 247  constructor
 248  · have h := pi_pow5_gt_d6
 249    exact le_of_lt (by calc ((3060193 / 10000 : ℚ) : ℝ) = (306.0193 : ℝ) := by norm_num
 250      _ < pi ^ 5 := h)
 251  · have h := pi_pow5_lt_d6
 252    exact le_of_lt (by calc pi ^ 5 < (306.0199 : ℝ) := h
 253      _ = ((3060199 / 10000 : ℚ) : ℝ) := by norm_num)
 254
 255end IndisputableMonolith.Numerics

depends on (5)

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