`BookProof.ChapterEulerNState.tailSum_nonneg` (p : ℕ → ℝ) (hp : ∀ k, 0 ≤ p k) (n k : ℕ) : 0 ≤ tailSum p n k

Proved

BookProof.ChapterEulerNState.tailSum_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerNState.

BookProof.ChapterEulerNState.tailSum_nonneg (p : ℕ → ℝ) (hp : ∀ k, 0 ≤ p k) (n k : ℕ) : 0 ≤ tailSum p n k

Formalization note: Lean 4 identifier BookProof.ChapterEulerNState.tailSum_nonneg.

Preamble

-- Generated from ChapterEulerNState.lean — theorem BookProof.ChapterEulerNState.tailSum_nonneg
import Mathlib
import Definitions.Def_ChapterEulerNState
open BookProof.ChapterEulerNState


open scoped BigOperators

Formal statement

theorem BookProof.ChapterEulerNState.tailSum_nonneg (p : ℕ → ℝ) (hp : ∀ k, 0 ≤ p k) (n k : ℕ) :
    0 ≤ tailSum p n k := by sorry

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