`BookProof.QuantumGravityHalfDensity.qgSrcMeasure_density_eq_halfDensity_sq` {y : ℝ} (hy : 0 ≤ y) : qgHalfDensity y ^ 2 = qgJacobian y

Proved

BookProof.QuantumGravityHalfDensity.qgSrcMeasure_density_eq_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_density_eq_halfDensity_sq {y : ℝ} (hy : 0 ≤ y) : qgHalfDensity y ^ 2 = qgJacobian y

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

Preamble

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



open MeasureTheory Set Filter
open scoped ENNReal

Formal statement

theorem BookProof.QuantumGravityHalfDensity.qgSrcMeasure_density_eq_halfDensity_sq {y : ℝ} (hy : 0 ≤ y) :
    qgHalfDensity y ^ 2 = qgJacobian y := by sorry

View graph