`BookProof.SmCar.car_annih_creat_of_ne` {i j : Fin n} (hij : i ≠ j) : annih i ∘ₗ creat j + creat j ∘ₗ annih i = 0

Proved

BookProof.SmCar.car_annih_creat_of_ne

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmCarAlgebra.

BookProof.SmCar.car_annih_creat_of_ne {i j : Fin n} (hij : i ≠ j) : annih i ∘ₗ creat j + creat j ∘ₗ annih i = 0

Formalization note: Lean 4 identifier BookProof.SmCar.car_annih_creat_of_ne.

Preamble

-- Generated from ChapterSmCarAlgebra.lean — theorem BookProof.SmCar.car_annih_creat_of_ne
import Mathlib
import Definitions.Def_ChapterSmCarAlgebra
import Definitions.Def_ChapterNavierStokesFockSpace
open BookProof.NavierStokesFlow.FockOfFock
open BookProof.SmCar



open Finset

variable {n : ℕ}

Formal statement

theorem BookProof.SmCar.car_annih_creat_of_ne {i j : Fin n} (hij : i ≠ j) :
    annih i ∘ₗ creat j + creat j ∘ₗ annih i = 0 := by sorry

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