Prove2Me

`BookProof.SmDiracYukawa.smFermiHam_norm_le` (hD M : Matrix (Fin n) (Fin n) ℂ) (z : ℂ) (ψ : FermiFock n) : ‖smFermiHam hD M z ψ‖ ≤ (∑ i : Fin n, ∑ j : Fin n, ‖smFermiMatrix hD M z

Proved
BookProof.SmDiracYukawa.smFermiHam_norm_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmDiracYukawa.

BookProof.SmDiracYukawa.smFermiHam_norm_le (hD M : Matrix (Fin n) (Fin n) ℂ) (z : ℂ) (ψ : FermiFock n) : ‖smFermiHam hD M z ψ‖ ≤ (∑ i : Fin n, ∑ j : Fin n, ‖smFermiMatrix hD M z i j‖) * ‖ψ‖

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

Preamble
-- Generated from ChapterSmDiracYukawa.lean — theorem BookProof.SmDiracYukawa.smFermiHam_norm_le
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_norm_le (hD M : Matrix (Fin n) (Fin n) ℂ) (z : ℂ) (ψ : FermiFock n) :
    ‖smFermiHam hD M z ψ‖
      ≤ (∑ i : Fin n, ∑ j : Fin n, ‖smFermiMatrix hD M z i j‖) * ‖ψ‖ := by sorry

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