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`BookProof.ChapterScaledDotProduct.sum_sgn_mul_self` (i : Fin d) : ∑ x : (Fin d → Bool), sgn (x i) * sgn (x i) = 2 ^ d

Proved
BookProof.ChapterScaledDotProduct.sum_sgn_mul_self

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScaledDotProduct.

BookProof.ChapterScaledDotProduct.sum_sgn_mul_self (i : Fin d) : ∑ x : (Fin d → Bool), sgn (x i) * sgn (x i) = 2 ^ d

Formalization note: Lean 4 identifier BookProof.ChapterScaledDotProduct.sum_sgn_mul_self.

Preamble
-- Generated from ChapterScaledDotProduct.lean — theorem BookProof.ChapterScaledDotProduct.sum_sgn_mul_self
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterScaledDotProduct
open BookProof.ChapterScaledDotProduct


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness

variable {d : ℕ}
Formal statement
theorem BookProof.ChapterScaledDotProduct.sum_sgn_mul_self (i : Fin d) :
    ∑ x : (Fin d → Bool), sgn (x i) * sgn (x i) = 2 ^ d := by sorry

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