Prove2Me

`BookProof.SmCar.fermiEnergy_apply` (m : Fin n → ℝ) (ψ : FermiFock n) (S : Finset (Fin n)) : (fermiEnergy m ψ) S = ((∑ i ∈ S, m i : ℝ) : ℂ) * ψ S

Proved
BookProof.SmCar.fermiEnergy_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmCarAlgebra.

BookProof.SmCar.fermiEnergy_apply (m : Fin n → ℝ) (ψ : FermiFock n) (S : Finset (Fin n)) : (fermiEnergy m ψ) S = ((∑ i ∈ S, m i : ℝ) : ℂ) * ψ S

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

Preamble
-- Generated from ChapterSmCarAlgebra.lean — theorem BookProof.SmCar.fermiEnergy_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.fermiEnergy_apply (m : Fin n → ℝ) (ψ : FermiFock n) (S : Finset (Fin n)) :
    (fermiEnergy m ψ) S = ((∑ i ∈ S, m i : ℝ) : ℂ) * ψ S := by sorry

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