`BookProof.ChapterTimeTranslation.trace_diagPart_measOp` (U : Matrix (Fin n) (Fin n) ℂ) (a : Fin n) (Ψ : Fin n → ℂ) : (diagPart (rho Ψ) * measOp U a).trace = ∑ k : Fin n, (starRing

Proved

BookProof.ChapterTimeTranslation.trace_diagPart_measOp

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTimeTranslation.

BookProof.ChapterTimeTranslation.trace_diagPart_measOp (U : Matrix (Fin n) (Fin n) ℂ) (a : Fin n) (Ψ : Fin n → ℂ) : (diagPart (rho Ψ) * measOp U a).trace = ∑ k : Fin n, (starRingEnd ℂ) (U k a) * Ψ k * (starRingEnd ℂ) (Ψ k) * U k a

Formalization note: Lean 4 identifier BookProof.ChapterTimeTranslation.trace_diagPart_measOp.

Preamble

-- Generated from ChapterTimeTranslation.lean — theorem BookProof.ChapterTimeTranslation.trace_diagPart_measOp
import Definitions.Def_ChapterReconstruct
import Mathlib
import Definitions.Def_ChapterTimeTranslation
open BookProof.ChapterTimeTranslation


open scoped BigOperators
open Finset Matrix
open BookProof.ChapterReconstruct


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterTimeTranslation.trace_diagPart_measOp (U : Matrix (Fin n) (Fin n) ℂ) (a : Fin n) (Ψ : Fin n → ℂ) :
    (diagPart (rho Ψ) * measOp U a).trace =
      ∑ k : Fin n,
        (starRingEnd ℂ) (U k a) * Ψ k * (starRingEnd ℂ) (Ψ k) * U k a := by sorry

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