Prove2Me

`BookProof.SmDiracYukawa.diagOp_inner` (d : Finset (Fin n) → ℝ) (ψ : FermiFock n) : (inner ℂ ψ (diagOp d ψ) : ℂ) = ∑ S : Finset (Fin n), ((d S * ‖ψ S‖ ^ 2 : ℝ) : ℂ)

Proved
BookProof.SmDiracYukawa.diagOp_inner

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmDiracYukawa.

BookProof.SmDiracYukawa.diagOp_inner (d : Finset (Fin n) → ℝ) (ψ : FermiFock n) : (inner ℂ ψ (diagOp d ψ) : ℂ) = ∑ S : Finset (Fin n), ((d S * ‖ψ S‖ ^ 2 : ℝ) : ℂ)

Formalization note: Lean 4 identifier BookProof.SmDiracYukawa.diagOp_inner.

Preamble
-- Generated from ChapterSmDiracYukawa.lean — theorem BookProof.SmDiracYukawa.diagOp_inner
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterSmDiracYukawa
import Definitions.Def_ChapterAbelianDiagonalCountable
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.ChapterAbelianDiagonalCountable
open BookProof.SmCar
open BookProof.SmDiracYukawa



open Finset Matrix
open BookProof.SmCar BookProof.FarisLavine

variable {n : ℕ}

noncomputable section
Formal statement
theorem BookProof.SmDiracYukawa.diagOp_inner (d : Finset (Fin n) → ℝ) (ψ : FermiFock n) :
    (inner ℂ ψ (diagOp d ψ) : ℂ)
      = ∑ S : Finset (Fin n), ((d S * ‖ψ S‖ ^ 2 : ℝ) : ℂ) := by sorry

View graph