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

-- Generated from ChapterQuantumGravity3DGauge.lean — theorem BookProof.QuantumGravity3DGauge.smul_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 {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {D : Submodule ℂ F}

theorem BookProof.QuantumGravity3DGauge.smul_symmetricOn {T : D →ₗ[ℂ] D} (r : ℝ)
    (hT : SymmetricOn D (D.subtype.comp T)) :
    SymmetricOn D (D.subtype.comp (((r : ℝ) : ℂ) • T)) := by sorry