Prove2Me

`BookProof.QuantumGravityFock.qgGhostCar_of_ne` {j k : ℕ} (h : j ≠ k) (z : QGGraded) : ghostOp (fermAnn j) (ghostOp (fermCre k) z) + ghostOp (fermCre k) (ghostOp (fermAnn j) z) = 0

Proved
BookProof.QuantumGravityFock.qgGhostCar_of_ne

by leonardopedro · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQuantumGravityFock.

BookProof.QuantumGravityFock.qgGhostCar_of_ne {j k : ℕ} (h : j ≠ k) (z : QGGraded) : ghostOp (fermAnn j) (ghostOp (fermCre k) z) + ghostOp (fermCre k) (ghostOp (fermAnn j) z) = 0

Formalization note: Lean 4 identifier BookProof.QuantumGravityFock.qgGhostCar_of_ne.

Preamble
-- Generated from ChapterQuantumGravityFock.lean — theorem BookProof.QuantumGravityFock.qgGhostCar_of_ne
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesFockSpace
import Definitions.Def_ChapterNavierStokesFullEsa
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterSirkTrotterKato
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
import Definitions.Def_ChapterComplexShiftCore
import Mathlib
import Definitions.Def_ChapterQuantumGravityFock
import Definitions.Def_ChapterFockSecondQuantization
open BookProof.FockSecondQuantization
open BookProof.QuantumGravityFock



open BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato
open BookProof.NavierStokesFlow.FockOfFock BookProof.NavierStokesFlow.FullEsa
open BookProof.FarisLavine BookProof.StoneBridge BookProof.EsaClosure
open BookProof.ChapterStoneResolvent BookProof.YangMillsFriedrichs
open BookProof.HermiteGalerkin BookProof.HashimotoShiftInvert
open BookProof.FockSecondQuantization

noncomputable section
Formal statement
theorem BookProof.QuantumGravityFock.qgGhostCar_of_ne {j k : ℕ} (h : j ≠ k) (z : QGGraded) :
    ghostOp (fermAnn j) (ghostOp (fermCre k) z) + ghostOp (fermCre k) (ghostOp (fermAnn j) z)
      = 0 := by sorry

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