`BookProof.ScalaronDensitized.densConfCore_dense` : Dense ((densConfCore M alpha : Submodule ℂ (Lp ℂ 2 qgSrcMeasure)) : Set (Lp ℂ 2 qgSrcMeasure))

Proved

BookProof.ScalaronDensitized.densConfCore_dense

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScalaronDensitizedTransfer.

BookProof.ScalaronDensitized.densConfCore_dense : Dense ((densConfCore M alpha : Submodule ℂ (Lp ℂ 2 qgSrcMeasure)) : Set (Lp ℂ 2 qgSrcMeasure))

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

Preamble

-- Generated from ChapterScalaronDensitizedTransfer.lean — theorem BookProof.ScalaronDensitized.densConfCore_dense
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterQuantumGravityDensitized
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_ChapterQuantumGravityHalfDensity
open BookProof.QuantumGravityHalfDensity
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.densConfCore_dense :
    Dense ((densConfCore M alpha : Submodule ℂ (Lp ℂ 2 qgSrcMeasure)) :
      Set (Lp ℂ 2 qgSrcMeasure)) := by sorry

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