Prove2Me

`BookProof.SmDiracYukawa.sm_fermi_fl_ii` (hom : ∀ i, 0 ≤ om i) (hc0 : 1 ≤ c0) (x : fullDom n) : |commForm (onFull (smFermiHam hD M z)) (onFull (smFermiN om c0)) x| ≤ (2 * smFermiBo

Proved
BookProof.SmDiracYukawa.sm_fermi_fl_ii

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmDiracYukawa.

BookProof.SmDiracYukawa.sm_fermi_fl_ii (hom : ∀ i, 0 ≤ om i) (hc0 : 1 ≤ c0) (x : fullDom n) : |commForm (onFull (smFermiHam hD M z)) (onFull (smFermiN om c0)) x| ≤ (2 * smFermiBound hD M z * smFermiOm om c0) * quadForm (onFull (smFermiN om c0)) x

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

Preamble
-- Generated from ChapterSmDiracYukawa.lean — theorem BookProof.SmDiracYukawa.sm_fermi_fl_ii
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterSmDiracYukawa
import Definitions.Def_ChapterFarisLavineCore
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.sm_fermi_fl_ii (hom : ∀ i, 0 ≤ om i) (hc0 : 1 ≤ c0) (x : fullDom n) :
    |commForm (onFull (smFermiHam hD M z)) (onFull (smFermiN om c0)) x|
      ≤ (2 * smFermiBound hD M z * smFermiOm om c0)
        * quadForm (onFull (smFermiN om c0)) x := by sorry

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