`BookProof.SmBrstGhost.annih_mul_creat` {N : ℕ} (p q : Fin N) : (annih p : Module.End ℂ (FermiFock N)) * creat q = (if p = q then 1 else 0) - creat q * annih p

Proved

BookProof.SmBrstGhost.annih_mul_creat

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmBrstGhost.

BookProof.SmBrstGhost.annih_mul_creat {N : ℕ} (p q : Fin N) : (annih p : Module.End ℂ (FermiFock N)) * creat q = (if p = q then 1 else 0) - creat q * annih p

Formalization note: Lean 4 identifier BookProof.SmBrstGhost.annih_mul_creat.

Preamble

-- Generated from ChapterSmBrstGhost.lean — theorem BookProof.SmBrstGhost.annih_mul_creat
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterYangMillsSU3
import Mathlib
import Definitions.Def_ChapterSmBrstGhost
import Definitions.Def_ChapterNavierStokesFockSpace
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.SmCar
open BookProof.SmBrstGhost



open BookProof.SmCar BookProof.BRSTNilpotent BookProof.YangMillsSU3

noncomputable section

variable {m : ℕ}

Formal statement

theorem BookProof.SmBrstGhost.annih_mul_creat {N : ℕ} (p q : Fin N) :
    (annih p : Module.End ℂ (FermiFock N)) * creat q
      = (if p = q then 1 else 0) - creat q * annih p := by sorry

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