`BookProof.ChapterConservative.timeEvo_conj_trace` (H : Matrix n n ℂ) (hH : H.IsHermitian) (t : ℝ) (ρ : Matrix n n ℂ) : (timeEvo H t * ρ * (timeEvo H t)ᴴ).trace = ρ.trace

Proved

BookProof.ChapterConservative.timeEvo_conj_trace

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterConservative.

BookProof.ChapterConservative.timeEvo_conj_trace (H : Matrix n n ℂ) (hH : H.IsHermitian) (t : ℝ) (ρ : Matrix n n ℂ) : (timeEvo H t * ρ * (timeEvo H t)ᴴ).trace = ρ.trace

Formalization note: Lean 4 identifier BookProof.ChapterConservative.timeEvo_conj_trace.

Preamble

-- Generated from ChapterConservative.lean — theorem BookProof.ChapterConservative.timeEvo_conj_trace
import Mathlib
import Definitions.Def_ChapterConservative
open BookProof.ChapterConservative


open scoped Matrix


variable {n : Type*} [Fintype n] [DecidableEq n]

Formal statement

theorem BookProof.ChapterConservative.timeEvo_conj_trace (H : Matrix n n ℂ) (hH : H.IsHermitian) (t : ℝ)
    (ρ : Matrix n n ℂ) :
    (timeEvo H t * ρ * (timeEvo H t)ᴴ).trace = ρ.trace := by sorry

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