`BookProof.ChapterBell.chsh_pointwise` {a₀ a₁ b₀ b₁ : ℝ} (ha₀ : |a₀| ≤ 1) (ha₁ : |a₁| ≤ 1) (hb₀ : |b₀| ≤ 1) (hb₁ : |b₁| ≤ 1) : |a₀ * b₀ + a₀ * b₁ + a₁...

Proved

BookProof.ChapterBell.chsh_pointwise

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBell.

BookProof.ChapterBell.chsh_pointwise {a₀ a₁ b₀ b₁ : ℝ} (ha₀ : |a₀| ≤ 1) (ha₁ : |a₁| ≤ 1) (hb₀ : |b₀| ≤ 1) (hb₁ : |b₁| ≤ 1) : |a₀ * b₀ + a₀ * b₁ + a₁ * b₀ - a₁ * b₁| ≤ 2

Formalization note: Lean 4 identifier BookProof.ChapterBell.chsh_pointwise.

Preamble

-- Generated from ChapterBell.lean — theorem BookProof.ChapterBell.chsh_pointwise
import Mathlib
import Definitions.Def_ChapterBell
open BookProof.ChapterBell


open scoped BigOperators
open MeasureTheory

Formal statement

theorem BookProof.ChapterBell.chsh_pointwise {a₀ a₁ b₀ b₁ : ℝ}
    (ha₀ : |a₀| ≤ 1) (ha₁ : |a₁| ≤ 1) (hb₀ : |b₀| ≤ 1) (hb₁ : |b₁| ≤ 1) :
    |a₀ * b₀ + a₀ * b₁ + a₁ * b₀ - a₁ * b₁| ≤ 2 := by sorry

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