`BookProof.ChapterThermalTemperatureCore.geometricMean_nonneg` (h0 : 0 ≤ r) (h1 : r < 1) : 0 ≤ geometricMean r

Proved

BookProof.ChapterThermalTemperatureCore.geometricMean_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterThermalTemperatureCore.

BookProof.ChapterThermalTemperatureCore.geometricMean_nonneg (h0 : 0 ≤ r) (h1 : r < 1) : 0 ≤ geometricMean r

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

Preamble

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


noncomputable section


open BookProof.ChapterCoherentTemperature BookProof.ChapterCoherentOccupation
open BookProof.ChapterBoseEinstein

variable {r : ℝ}

Formal statement

theorem BookProof.ChapterThermalTemperatureCore.geometricMean_nonneg (h0 : 0 ≤ r) (h1 : r < 1) : 0 ≤ geometricMean r := by sorry

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