Prove2Me

`BookProof.ChapterGaugeAdjointAlgebra.adj_closure` (θ η X : L) : adjVar η (adjVar θ X) - adjVar θ (adjVar η X) = adjVar ⁅θ, η⁆ X

Proved
BookProof.ChapterGaugeAdjointAlgebra.adj_closure

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeAdjointAlgebra.

BookProof.ChapterGaugeAdjointAlgebra.adj_closure (θ η X : L) : adjVar η (adjVar θ X) - adjVar θ (adjVar η X) = adjVar ⁅θ, η⁆ X

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

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




open Finset

variable {L : Type*} [LieRing L]
Formal statement
theorem BookProof.ChapterGaugeAdjointAlgebra.adj_closure (θ η X : L) :
    adjVar η (adjVar θ X) - adjVar θ (adjVar η X) = adjVar ⁅θ, η⁆ X := by sorry

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