`BookProof.ChapterThermalTemperatureCore.half_integer_floor_coherent` {lam : ℝ} (h : 0 ≤ lam) : 1 / 2 ≤ ∑' n : ℕ, ((n : ℝ) + 1 / 2) * coherentOccupation lam n

Proved

BookProof.ChapterThermalTemperatureCore.half_integer_floor_coherent

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterThermalTemperatureCore.

BookProof.ChapterThermalTemperatureCore.half_integer_floor_coherent {lam : ℝ} (h : 0 ≤ lam) : 1 / 2 ≤ ∑' n : ℕ, ((n : ℝ) + 1 / 2) * coherentOccupation lam n

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

Preamble

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


noncomputable section


open BookProof.ChapterCoherentTemperature BookProof.ChapterCoherentOccupation
open BookProof.ChapterBoseEinstein

variable {r : ℝ}

Formal statement

theorem BookProof.ChapterThermalTemperatureCore.half_integer_floor_coherent {lam : ℝ} (h : 0 ≤ lam) :
    1 / 2 ≤ ∑' n : ℕ, ((n : ℝ) + 1 / 2) * coherentOccupation lam n := by sorry

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