`BookProof.ChapterEulerCountableChain.stickProb_euler` (θ : ℕ → ℝ) (n : ℕ) : stickProb (condCos θ) n = (∏ k ∈ Finset.range n, Real.sin (θ k) ^ 2) * Real.cos (θ n) ^ 2

Proved

BookProof.ChapterEulerCountableChain.stickProb_euler

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerCountableChain.

BookProof.ChapterEulerCountableChain.stickProb_euler (θ : ℕ → ℝ) (n : ℕ) : stickProb (condCos θ) n = (∏ k ∈ Finset.range n, Real.sin (θ k) ^ 2) * Real.cos (θ n) ^ 2

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

Preamble

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


open scoped BigOperators
open Filter Topology

Formal statement

theorem BookProof.ChapterEulerCountableChain.stickProb_euler (θ : ℕ → ℝ) (n : ℕ) :
    stickProb (condCos θ) n
      = (∏ k ∈ Finset.range n, Real.sin (θ k) ^ 2) * Real.cos (θ n) ^ 2 := by sorry

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