Prove2Me

`BookProof.SmDiracYukawa.smFermiHam_symmetric` {hD M : Matrix (Fin n) (Fin n) ℂ} (z : ℂ) (hh : hD.conjTranspose = hD) (ψ φ : FermiFock n) : (inner ℂ (smFermiHam hD M z ψ) φ : ℂ) =

Proved
BookProof.SmDiracYukawa.smFermiHam_symmetric

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmDiracYukawa.

BookProof.SmDiracYukawa.smFermiHam_symmetric {hD M : Matrix (Fin n) (Fin n) ℂ} (z : ℂ) (hh : hD.conjTranspose = hD) (ψ φ : FermiFock n) : (inner ℂ (smFermiHam hD M z ψ) φ : ℂ) = inner ℂ ψ (smFermiHam hD M z φ)

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

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



open Finset Matrix
open BookProof.SmCar BookProof.FarisLavine

variable {n : ℕ}

noncomputable section
Formal statement
theorem BookProof.SmDiracYukawa.smFermiHam_symmetric {hD M : Matrix (Fin n) (Fin n) ℂ} (z : ℂ)
    (hh : hD.conjTranspose = hD) (ψ φ : FermiFock n) :
    (inner ℂ (smFermiHam hD M z ψ) φ : ℂ) = inner ℂ ψ (smFermiHam hD M z φ) := by sorry

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