Prove2Me

`BookProof.QuantumGravityBrstCharge.bosOp_ghostOp_comm` (S : Module.End ℂ qgPoly) (T : Module.End ℂ ghostSpace) : bosOp S * ghostOp T = ghostOp T * bosOp S

Proved
BookProof.QuantumGravityBrstCharge.bosOp_ghostOp_comm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQuantumGravityBrstCharge.

BookProof.QuantumGravityBrstCharge.bosOp_ghostOp_comm (S : Module.End ℂ qgPoly) (T : Module.End ℂ ghostSpace) : bosOp S * ghostOp T = ghostOp T * bosOp S

Formalization note: Lean 4 identifier BookProof.QuantumGravityBrstCharge.bosOp_ghostOp_comm.

Preamble
-- Generated from ChapterQuantumGravityBrstCharge.lean — theorem BookProof.QuantumGravityBrstCharge.bosOp_ghostOp_comm
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterYangMillsHermite
import Definitions.Def_ChapterQuantumGravity3DGauge
import Mathlib
import Definitions.Def_ChapterQuantumGravityBrstCharge
open BookProof.QuantumGravityBrstCharge



open MvPolynomial BookProof.BRSTNilpotent BookProof.YangMillsHermite
open BookProof.QuantumGravity3DGauge

noncomputable section

variable {R : Type*} [Ring R] [Algebra ℝ R] {n : ℕ}
variable {f : Fin n → Fin n → Fin n → ℝ} {G χ β : Fin n → R}
variable {d : ℕ}
variable {α : Type*}
Formal statement
theorem BookProof.QuantumGravityBrstCharge.bosOp_ghostOp_comm (S : Module.End ℂ qgPoly) (T : Module.End ℂ ghostSpace) :
    bosOp S * ghostOp T = ghostOp T * bosOp S := by sorry

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