`BookProof.SmCar.occupation_apply` (i : Fin n) (ψ : FermiFock n) (S : Finset (Fin n)) : (creat i (annih i ψ)) S = if i ∈ S then ψ S else 0

Proved

BookProof.SmCar.occupation_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmCarAlgebra.

BookProof.SmCar.occupation_apply (i : Fin n) (ψ : FermiFock n) (S : Finset (Fin n)) : (creat i (annih i ψ)) S = if i ∈ S then ψ S else 0

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

Preamble

-- Generated from ChapterSmCarAlgebra.lean — theorem BookProof.SmCar.occupation_apply
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.occupation_apply (i : Fin n) (ψ : FermiFock n) (S : Finset (Fin n)) :
    (creat i (annih i ψ)) S = if i ∈ S then ψ S else 0 := by sorry

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