`BookProof.YangMillsAbelianNoGap.magPoly_abelian` (i : Fin 3) (a : Fin 8) : magPoly (fun _ _ _ => 0) i a = ∑ j : Fin 3, ∑ k : Fin 3, ((levi i j k : ℝ) : ℂ) • X (idxD j k a)

Proved

BookProof.YangMillsAbelianNoGap.magPoly_abelian

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterYangMillsAbelianNoGap.

BookProof.YangMillsAbelianNoGap.magPoly_abelian (i : Fin 3) (a : Fin 8) : magPoly (fun _ _ _ => 0) i a = ∑ j : Fin 3, ∑ k : Fin 3, ((levi i j k : ℝ) : ℂ) • X (idxD j k a)

Formalization note: Lean 4 identifier BookProof.YangMillsAbelianNoGap.magPoly_abelian.

Preamble

-- Generated from ChapterYangMillsAbelianNoGap.lean — theorem BookProof.YangMillsAbelianNoGap.magPoly_abelian
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterGaussCoordCombo
import Definitions.Def_ChapterSqueezedGaussStates
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
import Mathlib
import Definitions.Def_ChapterYangMillsAbelianNoGap
import Definitions.Def_ChapterYangMillsHermite
open BookProof.YangMillsHermite
open BookProof.YangMillsAbelianNoGap



open MvPolynomial MeasureTheory
open BookProof.HermiteProductCore BookProof.GaussCoordCombo BookProof.SqueezedGaussStates
open BookProof.YangMillsHermite BookProof.FarisLavine BookProof.HermiteGalerkin

noncomputable section

variable {d : ℕ}

variable (vf : Fin d → ℝ) (Mf : Fin d → ℕ)

Formal statement

theorem BookProof.YangMillsAbelianNoGap.magPoly_abelian (i : Fin 3) (a : Fin 8) :
    magPoly (fun _ _ _ => 0) i a
      = ∑ j : Fin 3, ∑ k : Fin 3, ((levi i j k : ℝ) : ℂ) • X (idxD j k a) := by sorry

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