`BookProof.ChapterEulerCountableChain.stick_tsum_one` (c : ℕ → ℝ) (hc : ∀ n, 0 ≤ c n ∧ c n ≤ 1) (htail : Tendsto (stickTail c) atTop (𝓝 0)) : ∑' n, stickProb c n = 1

Proved

BookProof.ChapterEulerCountableChain.stick_tsum_one

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerCountableChain.

BookProof.ChapterEulerCountableChain.stick_tsum_one (c : ℕ → ℝ) (hc : ∀ n, 0 ≤ c n ∧ c n ≤ 1) (htail : Tendsto (stickTail c) atTop (𝓝 0)) : ∑' n, stickProb c n = 1

Formalization note: Lean 4 identifier BookProof.ChapterEulerCountableChain.stick_tsum_one.

Preamble

-- Generated from ChapterEulerCountableChain.lean — theorem BookProof.ChapterEulerCountableChain.stick_tsum_one
import Mathlib
import Definitions.Def_ChapterEulerCountableChain
open BookProof.ChapterEulerCountableChain


open scoped BigOperators
open Filter Topology

Formal statement

theorem BookProof.ChapterEulerCountableChain.stick_tsum_one (c : ℕ → ℝ) (hc : ∀ n, 0 ≤ c n ∧ c n ≤ 1)
    (htail : Tendsto (stickTail c) atTop (𝓝 0)) :
    ∑' n, stickProb c n = 1 := by sorry

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