Bennett Two Beta Factor sqrt mul lt half

Proved

D1Bound5.bennettTwoBetaFactor_sqrt_mul_lt_half

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

The normalized residual bound is strictly below one half once the exact beta expression has been derived; no estimate of a recurrence is assumed.

Preamble

import Lean.Elab.Tactic.Omega
import Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_BennettTwoBetaBound_Definitions

Formal statement

section
namespace D1Bound5




















theorem _root_.D1Bound5.bennettTwoBetaFactor_sqrt_mul_lt_half
    (η : ℝ) (hη0 : 0 ≤ η) (hη1 : η ≤ 1) (k : ℕ) (hk : 1 ≤ k) :
    Real.sqrt η * bennettTwoBetaFactor k < 1 / 2 := by sorry

end D1Bound5
end

Source

D1Bound5/BennettTwoBetaBound.lean, lines 116-128, SHA-256 6be0ec4b4373f2704cbfdc6beb52a3796d8063f1c67fa2c91242af5752323182. Project: https://github.com/tomislav-math/d1-bound5-lean

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