`BookProof.ScalaronDensitized.physConfOp_symmetricOn` : SymmetricOn (physConfCore M alpha) ((physConfCore M alpha).subtype.comp (physConfOp M alpha))

Proved

BookProof.ScalaronDensitized.physConfOp_symmetricOn

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScalaronDensitizedTransfer.

BookProof.ScalaronDensitized.physConfOp_symmetricOn : SymmetricOn (physConfCore M alpha) ((physConfCore M alpha).subtype.comp (physConfOp M alpha))

Formalization note: Lean 4 identifier BookProof.ScalaronDensitized.physConfOp_symmetricOn.

Preamble

-- Generated from ChapterScalaronDensitizedTransfer.lean — theorem BookProof.ScalaronDensitized.physConfOp_symmetricOn
import Definitions.Def_ChapterQuantumGravityDensitized
import Definitions.Def_ChapterQuantumGravityHalfDensity
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesFockContinuum
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterSirkTrotterKato
import Definitions.Def_ChapterEsaClosureCore
import Mathlib
import Definitions.Def_ChapterScalaronDensitizedTransfer
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterStarobinskyPotential
open BookProof.Starobinsky
open BookProof.ScalaronDensitized



open MeasureTheory Set Filter Topology
open BookProof.Starobinsky BookProof.QuantumGravityDensitized
open BookProof.QuantumGravityHalfDensity
open BookProof.NavierStokesFlow BookProof.NavierStokesFlow.FockContinuum
open BookProof.FarisLavine BookProof.StoneBridge
open BookProof.ChapterStoneResolvent BookProof.EsaClosure

noncomputable section

variable (M alpha : ℝ)

Formal statement

theorem BookProof.ScalaronDensitized.physConfOp_symmetricOn :
    SymmetricOn (physConfCore M alpha)
      ((physConfCore M alpha).subtype.comp (physConfOp M alpha)) := by sorry

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