`BookProof.SmCar.inner_eq_sum` (x y : FermiFock n) : (inner ℂ x y : ℂ) = ∑ S : Finset (Fin n), (starRingEnd ℂ) (x S) * y S

Proved

BookProof.SmCar.inner_eq_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmCarAlgebra.

BookProof.SmCar.inner_eq_sum (x y : FermiFock n) : (inner ℂ x y : ℂ) = ∑ S : Finset (Fin n), (starRingEnd ℂ) (x S) * y S

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

Preamble

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



open Finset

variable {n : ℕ}

Formal statement

theorem BookProof.SmCar.inner_eq_sum (x y : FermiFock n) :
    (inner ℂ x y : ℂ) = ∑ S : Finset (Fin n), (starRingEnd ℂ) (x S) * y S := by sorry

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