`BookProof.ChapterScaledDotProduct.rademacherMean_dot_sq` (k : Fin d → ℝ) : rademacherMean (fun x => (dot (signVec x) k) ^ 2) = ∑ i, (k i) ^ 2

Proved

BookProof.ChapterScaledDotProduct.rademacherMean_dot_sq

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScaledDotProduct.

BookProof.ChapterScaledDotProduct.rademacherMean_dot_sq (k : Fin d → ℝ) : rademacherMean (fun x => (dot (signVec x) k) ^ 2) = ∑ i, (k i) ^ 2

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

Preamble

-- Generated from ChapterScaledDotProduct.lean — theorem BookProof.ChapterScaledDotProduct.rademacherMean_dot_sq
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.rademacherMean_dot_sq (k : Fin d → ℝ) :
    rademacherMean (fun x => (dot (signVec x) k) ^ 2) = ∑ i, (k i) ^ 2 := by sorry

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