`BookProof.ScalaronDensitized.densConfV_bddBelow` {M alpha : ℝ} (halpha : 0 < alpha) : BddBelow (Set.range fun y => densConfV M alpha y)

Proved

BookProof.ScalaronDensitized.densConfV_bddBelow

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScalaronDensitizedTransfer.

BookProof.ScalaronDensitized.densConfV_bddBelow {M alpha : ℝ} (halpha : 0 < alpha) : BddBelow (Set.range fun y => densConfV M alpha y)

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

Preamble

-- Generated from ChapterScalaronDensitizedTransfer.lean — theorem BookProof.ScalaronDensitized.densConfV_bddBelow
import Definitions.Def_ChapterStarobinskyPotential
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
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

Formal statement

theorem BookProof.ScalaronDensitized.densConfV_bddBelow {M alpha : ℝ} (halpha : 0 < alpha) :
    BddBelow (Set.range fun y => densConfV M alpha y) := by sorry

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