theorem
proved
tactic proof
log_phi_lt_049
show as:
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formal statement (Lean)
62theorem log_phi_lt_049 : Real.log ((1 + Real.sqrt 5) / 2) < (0.49 : ℝ) := by
proof body
Tactic-mode proof.
63 have h := log_phi_in_interval
64 -- logPhiInterval.hi = 482/1000 < 0.49
65 have h1 : ((482 / 1000 : ℚ) : ℝ) < (0.49 : ℝ) := by norm_num
66 exact lt_of_le_of_lt h.2 h1
67
68/-- Example: Prove φ > 1.61 (using interval lo = 1618/1000) -/