`BookProof.ChapterGaugeAdjointAlgebra.gaussLaw_covariant` (A dπ π : Fin 3 → L) (θ : L) : ∑ i, (⁅dπ i, θ⁆ + (⁅⁅A i, θ⁆, π i⁆ + ⁅A i, ⁅π i, θ⁆⁆)) = ⁅gaussLaw A...

Proved

BookProof.ChapterGaugeAdjointAlgebra.gaussLaw_covariant

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeAdjointAlgebra.

BookProof.ChapterGaugeAdjointAlgebra.gaussLaw_covariant (A dπ π : Fin 3 → L) (θ : L) : ∑ i, (⁅dπ i, θ⁆ + (⁅⁅A i, θ⁆, π i⁆ + ⁅A i, ⁅π i, θ⁆⁆)) = ⁅gaussLaw A dπ π, θ⁆

Formalization note: Lean 4 identifier BookProof.ChapterGaugeAdjointAlgebra.gaussLaw_covariant.

Preamble

-- Generated from ChapterGaugeAdjointAlgebra.lean — theorem BookProof.ChapterGaugeAdjointAlgebra.gaussLaw_covariant
import Mathlib
import Definitions.Def_ChapterGaugeAdjointAlgebra
open BookProof.ChapterGaugeAdjointAlgebra




open Finset

variable {L : Type*} [LieRing L]

Formal statement

theorem BookProof.ChapterGaugeAdjointAlgebra.gaussLaw_covariant (A dπ π : Fin 3 → L) (θ : L) :
    ∑ i, (⁅dπ i, θ⁆ + (⁅⁅A i, θ⁆, π i⁆ + ⁅A i, ⁅π i, θ⁆⁆))
      = ⁅gaussLaw A dπ π, θ⁆ := by sorry

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