`BookProof.SmDiracYukawa.dcommOp_apply` (H N : FermiFock n →ₗ[ℂ] FermiFock n) (ψ : FermiFock n) : dcommOp H N ψ = N (N (H ψ)) - N (H (N ψ)) - (N (H (N ψ)) - H (N (N ψ)))

Proved

BookProof.SmDiracYukawa.dcommOp_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmDiracYukawa.

BookProof.SmDiracYukawa.dcommOp_apply (H N : FermiFock n →ₗ[ℂ] FermiFock n) (ψ : FermiFock n) : dcommOp H N ψ = N (N (H ψ)) - N (H (N ψ)) - (N (H (N ψ)) - H (N (N ψ)))

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

Preamble

-- Generated from ChapterSmDiracYukawa.lean — theorem BookProof.SmDiracYukawa.dcommOp_apply
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

variable {hD M : Matrix (Fin n) (Fin n) ℂ} {z : ℂ} {om : Fin n → ℝ} {c0 : ℝ}

Formal statement

theorem BookProof.SmDiracYukawa.dcommOp_apply (H N : FermiFock n →ₗ[ℂ] FermiFock n) (ψ : FermiFock n) :
    dcommOp H N ψ = N (N (H ψ)) - N (H (N ψ)) - (N (H (N ψ)) - H (N (N ψ))) := by sorry

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