Prove2Me

`BookProof.ChapterThermalTemperatureCore.geometricOccupancy_eq_thermalProb` (h0 : 0 ≤ r) (h1 : r < 1) (n : ℕ) : geometricOccupancy r n = thermalProb (geometricMean r) n

Proved
BookProof.ChapterThermalTemperatureCore.geometricOccupancy_eq_thermalProb

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterThermalTemperatureCore.

BookProof.ChapterThermalTemperatureCore.geometricOccupancy_eq_thermalProb (h0 : 0 ≤ r) (h1 : r < 1) (n : ℕ) : geometricOccupancy r n = thermalProb (geometricMean r) n

Formalization note: Lean 4 identifier BookProof.ChapterThermalTemperatureCore.geometricOccupancy_eq_thermalProb.

Preamble
-- Generated from ChapterThermalTemperatureCore.lean — theorem BookProof.ChapterThermalTemperatureCore.geometricOccupancy_eq_thermalProb
import Definitions.Def_ChapterCoherentOccupation
import Definitions.Def_ChapterBoseEinstein
import Mathlib
import Definitions.Def_ChapterThermalTemperatureCore
import Definitions.Def_ChapterCoherentTemperature
open BookProof.ChapterCoherentTemperature
open BookProof.ChapterThermalTemperatureCore


noncomputable section


open BookProof.ChapterCoherentTemperature BookProof.ChapterCoherentOccupation
open BookProof.ChapterBoseEinstein

variable {r : ℝ}
Formal statement
theorem BookProof.ChapterThermalTemperatureCore.geometricOccupancy_eq_thermalProb (h0 : 0 ≤ r) (h1 : r < 1) (n : ℕ) :
    geometricOccupancy r n = thermalProb (geometricMean r) n := by sorry

View graph