`BookProof.ConservativeDiagonal.commutes_all_events_iff_isDiag` (H : Matrix n n ℂ) : (∀ S : Finset n, bracket H (eventProj S) = 0) ↔ H.IsDiag

Proved

BookProof.ConservativeDiagonal.commutes_all_events_iff_isDiag

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterConservativeDiagonal.

BookProof.ConservativeDiagonal.commutes_all_events_iff_isDiag (H : Matrix n n ℂ) : (∀ S : Finset n, bracket H (eventProj S) = 0) ↔ H.IsDiag

Formalization note: Lean 4 identifier BookProof.ConservativeDiagonal.commutes_all_events_iff_isDiag.

Preamble

-- Generated from ChapterConservativeDiagonal.lean — theorem BookProof.ConservativeDiagonal.commutes_all_events_iff_isDiag
import Mathlib
import Definitions.Def_ChapterConservativeDiagonal
import Definitions.Def_ChapterFreeFieldConstraint
open BookProof.FreeFieldConstraint
open BookProof.ConservativeDiagonal


open scoped Matrix
open Matrix BookProof.FreeFieldConstraint


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

Formal statement

theorem BookProof.ConservativeDiagonal.commutes_all_events_iff_isDiag (H : Matrix n n ℂ) :
    (∀ S : Finset n, bracket H (eventProj S) = 0) ↔ H.IsDiag := by sorry

View graph