`BookProof.ChapterDisplacedThermalOverlap.thermal_plus_zeroPoint_conv` (nbar : ℝ≥0) : (gaussianReal 0 nbar) ∗ (gaussianReal 0 (1 / 2)) = gaussianReal 0 (tauNN nbar)

Proved

BookProof.ChapterDisplacedThermalOverlap.thermal_plus_zeroPoint_conv

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDisplacedThermalOverlap.

BookProof.ChapterDisplacedThermalOverlap.thermal_plus_zeroPoint_conv (nbar : ℝ≥0) : (gaussianReal 0 nbar) ∗ (gaussianReal 0 (1 / 2)) = gaussianReal 0 (tauNN nbar)

Formalization note: Lean 4 identifier BookProof.ChapterDisplacedThermalOverlap.thermal_plus_zeroPoint_conv.

Preamble

-- Generated from ChapterDisplacedThermalOverlap.lean — theorem BookProof.ChapterDisplacedThermalOverlap.thermal_plus_zeroPoint_conv
import Mathlib
import Definitions.Def_ChapterDisplacedThermalOverlap
open BookProof.ChapterDisplacedThermalOverlap


noncomputable section

open MeasureTheory ProbabilityTheory Real
open scoped NNReal

Formal statement

theorem BookProof.ChapterDisplacedThermalOverlap.thermal_plus_zeroPoint_conv (nbar : ℝ≥0) :
    (gaussianReal 0 nbar) ∗ (gaussianReal 0 (1 / 2)) = gaussianReal 0 (tauNN nbar) := by sorry

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