`BookProof.ConservativeDiagonal.bracket_eventProj_apply` (H : Matrix n n ℂ) (S : Finset n) (k l : n) : bracket H (eventProj S) k l = H k l * ((if l ∈ S then (1 : ℂ) else 0) - (if k

Proved

BookProof.ConservativeDiagonal.bracket_eventProj_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterConservativeDiagonal.

BookProof.ConservativeDiagonal.bracket_eventProj_apply (H : Matrix n n ℂ) (S : Finset n) (k l : n) : bracket H (eventProj S) k l = H k l * ((if l ∈ S then (1 : ℂ) else 0) - (if k ∈ S then (1 : ℂ) else 0))

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

Preamble

-- Generated from ChapterConservativeDiagonal.lean — theorem BookProof.ConservativeDiagonal.bracket_eventProj_apply
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.bracket_eventProj_apply (H : Matrix n n ℂ) (S : Finset n) (k l : n) :
    bracket H (eventProj S) k l
      = H k l * ((if l ∈ S then (1 : ℂ) else 0) - (if k ∈ S then (1 : ℂ) else 0)) := by sorry

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