`BookProof.QuantumGravityHalfDensity.qgSrcMeasure_eq_withDensity_halfDensity_sq` : qgSrcMeasure = (volume.restrict (Set.Ioi (0 : ℝ))).withDensity fun y => ENNReal.ofReal (qgHalfDen

Proved

BookProof.QuantumGravityHalfDensity.qgSrcMeasure_eq_withDensity_halfDensity_sq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQuantumGravityHalfDensity.

BookProof.QuantumGravityHalfDensity.qgSrcMeasure_eq_withDensity_halfDensity_sq : qgSrcMeasure = (volume.restrict (Set.Ioi (0 : ℝ))).withDensity fun y => ENNReal.ofReal (qgHalfDensity y ^ 2)

Formalization note: Lean 4 identifier BookProof.QuantumGravityHalfDensity.qgSrcMeasure_eq_withDensity_halfDensity_sq.

Preamble

-- Generated from ChapterQuantumGravityHalfDensity.lean — theorem BookProof.QuantumGravityHalfDensity.qgSrcMeasure_eq_withDensity_halfDensity_sq
import Mathlib
import Definitions.Def_ChapterQuantumGravityHalfDensity
open BookProof.QuantumGravityHalfDensity



open MeasureTheory Set Filter
open scoped ENNReal

Formal statement

theorem BookProof.QuantumGravityHalfDensity.qgSrcMeasure_eq_withDensity_halfDensity_sq :
    qgSrcMeasure
      = (volume.restrict (Set.Ioi (0 : ℝ))).withDensity
          fun y => ENNReal.ofReal (qgHalfDensity y ^ 2) := by sorry

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