Prove2Me

`BookProof.ChapterF4.countsketch_unbiased` (h : Fin d → Fin k) (x y : Fin d → ℝ) : expectation (fun ω => ∑ j, csketch h ω x j * csketch h ω y j) = ∑ c, x c * y c

Proved
BookProof.ChapterF4.countsketch_unbiased

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF4.

BookProof.ChapterF4.countsketch_unbiased (h : Fin d → Fin k) (x y : Fin d → ℝ) : expectation (fun ω => ∑ j, csketch h ω x j * csketch h ω y j) = ∑ c, x c * y c

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

Preamble
-- Generated from ChapterF4.lean — theorem BookProof.ChapterF4.countsketch_unbiased
import Mathlib
import Definitions.Def_ChapterF4
import Definitions.Def_ChapterObservableOperator
import Definitions.Def_ChapterScaledDotProduct
open BookProof.ChapterObservableOperator
open BookProof.ChapterScaledDotProduct
open BookProof.ChapterF4


open scoped BigOperators Matrix

variable {d k : ℕ}
Formal statement
theorem BookProof.ChapterF4.countsketch_unbiased (h : Fin d → Fin k) (x y : Fin d → ℝ) :
    expectation (fun ω => ∑ j, csketch h ω x j * csketch h ω y j) = ∑ c, x c * y c := by sorry

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