`BookProof.ChapterWeakValue.weakValue_diag_isReal` (i : Fin n → ℂ) (A : Matrix (Fin n) (Fin n) ℂ) (hA : Aᴴ = A) (hi : ip i i = 1) : starRingEnd ℂ (weakValue i i A) = weakValue i i

Proved

BookProof.ChapterWeakValue.weakValue_diag_isReal

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeakValue.

BookProof.ChapterWeakValue.weakValue_diag_isReal (i : Fin n → ℂ) (A : Matrix (Fin n) (Fin n) ℂ) (hA : Aᴴ = A) (hi : ip i i = 1) : starRingEnd ℂ (weakValue i i A) = weakValue i i A

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

Preamble

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


open scoped BigOperators Matrix


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterWeakValue.weakValue_diag_isReal (i : Fin n → ℂ) (A : Matrix (Fin n) (Fin n) ℂ)
    (hA : Aᴴ = A) (hi : ip i i = 1) :
    starRingEnd ℂ (weakValue i i A) = weakValue i i A := by sorry

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