`BookProof.ChapterF4.csketch_smul` (h : Fin d → Fin k) (ω : Fin d → Bool) (a : ℝ) (x : Fin d → ℝ) : csketch h ω (a • x) = a • csketch h ω x

Proved

BookProof.ChapterF4.csketch_smul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF4.

BookProof.ChapterF4.csketch_smul (h : Fin d → Fin k) (ω : Fin d → Bool) (a : ℝ) (x : Fin d → ℝ) : csketch h ω (a • x) = a • csketch h ω x

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

Preamble

-- Generated from ChapterF4.lean — theorem BookProof.ChapterF4.csketch_smul
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.csketch_smul (h : Fin d → Fin k) (ω : Fin d → Bool) (a : ℝ) (x : Fin d → ℝ) :
    csketch h ω (a • x) = a • csketch h ω x := by sorry

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