`BookProof.ChapterScaledDotProduct.sum_sgn_mul_eq_zero` {i j : Fin d} (hij : i ≠ j) : ∑ x : (Fin d → Bool), sgn (x i) * sgn (x j) = 0

Proved

BookProof.ChapterScaledDotProduct.sum_sgn_mul_eq_zero

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_eq_zero {i j : Fin d} (hij : i ≠ j) : ∑ x : (Fin d → Bool), sgn (x i) * sgn (x j) = 0

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

Preamble

-- Generated from ChapterScaledDotProduct.lean — theorem BookProof.ChapterScaledDotProduct.sum_sgn_mul_eq_zero
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_eq_zero {i j : Fin d} (hij : i ≠ j) :
    ∑ x : (Fin d → Bool), sgn (x i) * sgn (x j) = 0 := by sorry

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