The Lean 4 theorem `qgWeylProd_symmetricOn` in the `ChapterQuantumGravity3DGauge` chapter of the timepiece formalization

Proved

BookProof.QuantumGravity3DGauge.qgWeylProd_symmetricOn

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

timepiece

The Lean 4 theorem qgWeylProd_symmetricOn in the ChapterQuantumGravity3DGauge chapter of the timepiece formalization.

Preamble

-- Generated from ChapterQuantumGravity3DGauge.lean — theorem BookProof.QuantumGravity3DGauge.qgWeylProd_symmetricOn
import Mathlib
import Definitions.Def_ChapterQuantumGravity3DGauge
open BookProof.QuantumGravity3DGauge



open MeasureTheory Complex MvPolynomial Filter Topology
open BookProof.HermiteProductCore BookProof.YangMillsHermite BookProof.YangMillsFriedrichs
open BookProof.FarisLavine BookProof.FriedrichsExtension BookProof.HermiteGalerkin
open BookProof.HashimotoShiftInvert BookProof.QuantumGravityDensitized

noncomputable section

variable {D : Submodule ℂ (L2d 84)}

Formal statement

theorem BookProof.QuantumGravity3DGauge.qgWeylProd_symmetricOn (Φ : CoreRep 84 D) (j k : Fin 84) :
    SymmetricOn D (D.subtype.comp (Φ.op (qgWeylProd (mulOp (X j)) (momOp k)))) := by sorry

Source

https://github.com/leonardopedro/timepiece/blob/61595bc/BookProof/ChapterQuantumGravity3DGauge.lean

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