`BookProof.ChapterE2.remainder_succ` (θ : ℕ → ℝ) (N : ℕ) : remainder θ (N + 1) = remainder θ N * Real.sin (θ N) ^ 2

Proved

BookProof.ChapterE2.remainder_succ

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterE2.

BookProof.ChapterE2.remainder_succ (θ : ℕ → ℝ) (N : ℕ) : remainder θ (N + 1) = remainder θ N * Real.sin (θ N) ^ 2

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

Preamble

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


open scoped BigOperators
open Finset

Formal statement

theorem BookProof.ChapterE2.remainder_succ (θ : ℕ → ℝ) (N : ℕ) :
    remainder θ (N + 1) = remainder θ N * Real.sin (θ N) ^ 2 := by sorry

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