`BookProof.ChapterEulerNState.tailProd_succ` (θ : ℕ → ℝ) (m : ℕ) : tailProd θ (m + 1) = tailProd θ m * Real.sin (θ m) ^ 2

Proved

BookProof.ChapterEulerNState.tailProd_succ

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerNState.

BookProof.ChapterEulerNState.tailProd_succ (θ : ℕ → ℝ) (m : ℕ) : tailProd θ (m + 1) = tailProd θ m * Real.sin (θ m) ^ 2

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

Preamble

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


open scoped BigOperators

Formal statement

theorem BookProof.ChapterEulerNState.tailProd_succ (θ : ℕ → ℝ) (m : ℕ) :
    tailProd θ (m + 1) = tailProd θ m * Real.sin (θ m) ^ 2 := by sorry

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