`BookProof.SmCar.normSq_eq_sum` (x : FermiFock n) : ‖x‖ ^ 2 = ∑ S : Finset (Fin n), ‖x S‖ ^ 2

Proved

BookProof.SmCar.normSq_eq_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmCarAlgebra.

BookProof.SmCar.normSq_eq_sum (x : FermiFock n) : ‖x‖ ^ 2 = ∑ S : Finset (Fin n), ‖x S‖ ^ 2

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

Preamble

-- Generated from ChapterSmCarAlgebra.lean — theorem BookProof.SmCar.normSq_eq_sum
import Mathlib
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.SmCar



open Finset

variable {n : ℕ}

Formal statement

theorem BookProof.SmCar.normSq_eq_sum (x : FermiFock n) :
    ‖x‖ ^ 2 = ∑ S : Finset (Fin n), ‖x S‖ ^ 2 := by sorry

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