`BookProof.ChapterWeakValue.weakValue_wellDefined` (i f : Fin n → ℂ) (A : Matrix (Fin n) (Fin n) ℂ) (h : ip f i ≠ 0) : weakValue i f A * ip f i = ip f (A *ᵥ i)

Proved

BookProof.ChapterWeakValue.weakValue_wellDefined

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakValue.

BookProof.ChapterWeakValue.weakValue_wellDefined (i f : Fin n → ℂ) (A : Matrix (Fin n) (Fin n) ℂ) (h : ip f i ≠ 0) : weakValue i f A * ip f i = ip f (A *ᵥ i)

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

Preamble

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


open scoped BigOperators Matrix


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterWeakValue.weakValue_wellDefined (i f : Fin n → ℂ) (A : Matrix (Fin n) (Fin n) ℂ)
    (h : ip f i ≠ 0) : weakValue i f A * ip f i = ip f (A *ᵥ i) := by sorry

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