`BookProof.ChapterWeakValue.weakValue_proj_sum` (i f : Fin n → ℂ) (h : ip f i ≠ 0) : ∑ a, weakValue i f (projMat a) = 1

Proved

BookProof.ChapterWeakValue.weakValue_proj_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakValue.

BookProof.ChapterWeakValue.weakValue_proj_sum (i f : Fin n → ℂ) (h : ip f i ≠ 0) : ∑ a, weakValue i f (projMat a) = 1

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

Preamble

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


open scoped BigOperators Matrix


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterWeakValue.weakValue_proj_sum (i f : Fin n → ℂ) (h : ip f i ≠ 0) :
    ∑ a, weakValue i f (projMat a) = 1 := by sorry

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