`BookProof.ChapterGaugeAdjointAlgebra.gaussLaw_constraint_surface_invariant` (A dπ π : Fin 3 → L) (θ : L) (hG : gaussLaw A dπ π = 0) : ∑ i, (⁅dπ i, θ⁆ + (⁅⁅A i, θ⁆, π i⁆...

Proved

BookProof.ChapterGaugeAdjointAlgebra.gaussLaw_constraint_surface_invariant

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeAdjointAlgebra.

BookProof.ChapterGaugeAdjointAlgebra.gaussLaw_constraint_surface_invariant (A dπ π : Fin 3 → L) (θ : L) (hG : gaussLaw A dπ π = 0) : ∑ i, (⁅dπ i, θ⁆ + (⁅⁅A i, θ⁆, π i⁆ + ⁅A i, ⁅π i, θ⁆⁆)) = 0

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

Preamble

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




open Finset

variable {L : Type*} [LieRing L]

Formal statement

theorem BookProof.ChapterGaugeAdjointAlgebra.gaussLaw_constraint_surface_invariant (A dπ π : Fin 3 → L) (θ : L)
    (hG : gaussLaw A dπ π = 0) :
    ∑ i, (⁅dπ i, θ⁆ + (⁅⁅A i, θ⁆, π i⁆ + ⁅A i, ⁅π i, θ⁆⁆)) = 0 := by sorry

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