`BookProof.ChapterF4.sign_pair_expectation` (c c' : Fin d) : (∑ ω : Fin d → Bool, sgn (ω c) * sgn (ω c')) = if c = c' then (2 ^ d : ℝ) else 0

Proved

BookProof.ChapterF4.sign_pair_expectation

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF4.

BookProof.ChapterF4.sign_pair_expectation (c c' : Fin d) : (∑ ω : Fin d → Bool, sgn (ω c) * sgn (ω c')) = if c = c' then (2 ^ d : ℝ) else 0

Formalization note: Lean 4 identifier BookProof.ChapterF4.sign_pair_expectation.

Preamble

-- Generated from ChapterF4.lean — theorem BookProof.ChapterF4.sign_pair_expectation
import Mathlib
import Definitions.Def_ChapterF4
import Definitions.Def_ChapterScaledDotProduct
open BookProof.ChapterScaledDotProduct
open BookProof.ChapterF4


open scoped BigOperators Matrix

variable {d k : ℕ}

Formal statement

theorem BookProof.ChapterF4.sign_pair_expectation (c c' : Fin d) :
    (∑ ω : Fin d → Bool, sgn (ω c) * sgn (ω c')) = if c = c' then (2 ^ d : ℝ) else 0 := by sorry

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