`BookProof.ChapterE2.sum_stick_add_remainder` (θ : ℕ → ℝ) (N : ℕ) : (∑ n ∈ range N, stick θ n) + remainder θ N = 1

Proved

BookProof.ChapterE2.sum_stick_add_remainder

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterE2.

BookProof.ChapterE2.sum_stick_add_remainder (θ : ℕ → ℝ) (N : ℕ) : (∑ n ∈ range N, stick θ n) + remainder θ N = 1

Formalization note: Lean 4 identifier BookProof.ChapterE2.sum_stick_add_remainder.

Preamble

-- Generated from ChapterE2.lean — theorem BookProof.ChapterE2.sum_stick_add_remainder
import Mathlib
import Definitions.Def_ChapterE2
open BookProof.ChapterE2


open scoped BigOperators
open Finset

Formal statement

theorem BookProof.ChapterE2.sum_stick_add_remainder (θ : ℕ → ℝ) (N : ℕ) :
    (∑ n ∈ range N, stick θ n) + remainder θ N = 1 := by sorry

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