`BookProof.SmDiracSpinor.smFermiHam_zero_yukawa` (hD : Matrix (Fin 4) (Fin 4) ℂ) : smFermiHam hD (0 : Matrix (Fin 4) (Fin 4) ℂ) 0 = fermiBilin hD

Proved

BookProof.SmDiracSpinor.smFermiHam_zero_yukawa

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmDiracSpinor.

BookProof.SmDiracSpinor.smFermiHam_zero_yukawa (hD : Matrix (Fin 4) (Fin 4) ℂ) : smFermiHam hD (0 : Matrix (Fin 4) (Fin 4) ℂ) 0 = fermiBilin hD

Formalization note: Lean 4 identifier BookProof.SmDiracSpinor.smFermiHam_zero_yukawa.

Preamble

-- Generated from ChapterSmDiracSpinor.lean — theorem BookProof.SmDiracSpinor.smFermiHam_zero_yukawa
import Definitions.Def_ChapterCPTHamiltonian
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterSmDiracSpinor
import Definitions.Def_ChapterSmCarAlgebra
import Definitions.Def_ChapterSmDiracYukawa
open BookProof.SmCar
open BookProof.SmDiracYukawa
open BookProof.SmDiracSpinor



open Matrix
open BookProof.ChapterCPTHamiltonian BookProof.SmCar BookProof.SmDiracYukawa
open BookProof.FarisLavine

noncomputable section

variable {k : Fin 3 → ℝ} {m1 m2 : ℝ}

Formal statement

theorem BookProof.SmDiracSpinor.smFermiHam_zero_yukawa (hD : Matrix (Fin 4) (Fin 4) ℂ) :
    smFermiHam hD (0 : Matrix (Fin 4) (Fin 4) ℂ) 0 = fermiBilin hD := by sorry

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