`BookProof.ChapterWeakValue.weakValue_linear` (c d : ℂ) (i f : Fin n → ℂ) (A B : Matrix (Fin n) (Fin n) ℂ) : weakValue i f (c • A + d • B) = c * weakValue i f A + d * weakValue i f

Proved

BookProof.ChapterWeakValue.weakValue_linear

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakValue.

BookProof.ChapterWeakValue.weakValue_linear (c d : ℂ) (i f : Fin n → ℂ) (A B : Matrix (Fin n) (Fin n) ℂ) : weakValue i f (c • A + d • B) = c * weakValue i f A + d * weakValue i f B

Formalization note: Lean 4 identifier BookProof.ChapterWeakValue.weakValue_linear.

Preamble

-- Generated from ChapterWeakValue.lean — theorem BookProof.ChapterWeakValue.weakValue_linear
import Mathlib
import Definitions.Def_ChapterWeakValue
open BookProof.ChapterWeakValue


open scoped BigOperators Matrix


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterWeakValue.weakValue_linear (c d : ℂ) (i f : Fin n → ℂ)
    (A B : Matrix (Fin n) (Fin n) ℂ) :
    weakValue i f (c • A + d • B) =
      c * weakValue i f A + d * weakValue i f B := by sorry

View graph