`BookProof.ChapterWeakValue.projMat_mulVec` (a : Fin n) (v : Fin n → ℂ) (b : Fin n) : (projMat a *ᵥ v) b = if b = a then v a else 0

Proved

BookProof.ChapterWeakValue.projMat_mulVec

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakValue.

BookProof.ChapterWeakValue.projMat_mulVec (a : Fin n) (v : Fin n → ℂ) (b : Fin n) : (projMat a *ᵥ v) b = if b = a then v a else 0

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

Preamble

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


open scoped BigOperators Matrix


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterWeakValue.projMat_mulVec (a : Fin n) (v : Fin n → ℂ) (b : Fin n) :
    (projMat a *ᵥ v) b = if b = a then v a else 0 := by sorry

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