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`BookProof.ChapterGaugeAdjointAlgebra.lie_adj_leibniz` (x θ y : L) : ⁅⁅x, θ⁆, y⁆ + ⁅x, ⁅y, θ⁆⁆ = ⁅⁅x, y⁆, θ⁆

Proved
BookProof.ChapterGaugeAdjointAlgebra.lie_adj_leibniz

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeAdjointAlgebra.

BookProof.ChapterGaugeAdjointAlgebra.lie_adj_leibniz (x θ y : L) : ⁅⁅x, θ⁆, y⁆ + ⁅x, ⁅y, θ⁆⁆ = ⁅⁅x, y⁆, θ⁆

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

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




open Finset

variable {L : Type*} [LieRing L]
Formal statement
theorem BookProof.ChapterGaugeAdjointAlgebra.lie_adj_leibniz (x θ y : L) : ⁅⁅x, θ⁆, y⁆ + ⁅x, ⁅y, θ⁆⁆ = ⁅⁅x, y⁆, θ⁆ := by sorry

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