roth_lower_bound — Mathlib

English

If N ≥ 64, then 3 ≤ nValue(N).

Русский

Если N ≥ 64, то 3 ≤ nValue(N).

LaTeX

$$$$ N \\ge 64 \\Rightarrow 3 \\le nValue(N). $$$$

Lean4

theorem roth_lower_bound : (N : ℝ) * exp (-4 * √(log N)) ≤ rothNumberNat N :=
  by
  obtain rfl | hN := Nat.eq_zero_or_pos N
  · simp
  obtain h₁ | h₁ := le_or_gt 4096 N
  · exact (roth_lower_bound_explicit h₁).le
  · apply (lower_bound_le_one hN h₁.le).trans
    simpa using rothNumberNat.monotone hN

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