`BookProof.SmDiracYukawa.yukawa_entry_bound` {UL V UR D : Matrix (Fin 3) (Fin 3) ℂ} (hUL : IsMixing UL) (hV : IsMixing V) (hUR : IsMixing UR) (hD : ∀ k l, k ≠ l → D k l = 0) (i j :

Proved

BookProof.SmDiracYukawa.yukawa_entry_bound

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmDiracYukawa.

BookProof.SmDiracYukawa.yukawa_entry_bound {UL V UR D : Matrix (Fin 3) (Fin 3) ℂ} (hUL : IsMixing UL) (hV : IsMixing V) (hUR : IsMixing UR) (hD : ∀ k l, k ≠ l → D k l = 0) (i j : Fin 3) : ‖(UL * V.conjTranspose * D * UR.conjTranspose) i j‖ ≤ ∑ k : Fin 3, ‖D k k‖

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

Preamble

-- Generated from ChapterSmDiracYukawa.lean — theorem BookProof.SmDiracYukawa.yukawa_entry_bound
import Definitions.Def_ChapterSmCarAlgebra
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterSmDiracYukawa
import Definitions.Def_ChapterSmOneParticle
open BookProof.SmOneParticle
open BookProof.SmDiracYukawa



open Finset Matrix
open BookProof.SmCar BookProof.FarisLavine

variable {n : ℕ}

noncomputable section

open BookProof.SmOneParticle

Formal statement

theorem BookProof.SmDiracYukawa.yukawa_entry_bound {UL V UR D : Matrix (Fin 3) (Fin 3) ℂ}
    (hUL : IsMixing UL) (hV : IsMixing V) (hUR : IsMixing UR)
    (hD : ∀ k l, k ≠ l → D k l = 0) (i j : Fin 3) :
    ‖(UL * V.conjTranspose * D * UR.conjTranspose) i j‖ ≤ ∑ k : Fin 3, ‖D k k‖ := by sorry

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