`BookProof.ChapterE4.cond_prob_sum` (θ : ℕ → ℝ) (s : ℕ) : Real.cos (θ s) ^ 2 + Real.sin (θ s) ^ 2 = 1

Proved

BookProof.ChapterE4.cond_prob_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterE4.

BookProof.ChapterE4.cond_prob_sum (θ : ℕ → ℝ) (s : ℕ) : Real.cos (θ s) ^ 2 + Real.sin (θ s) ^ 2 = 1

Formalization note: Lean 4 identifier BookProof.ChapterE4.cond_prob_sum.

Preamble

-- Generated from ChapterE4.lean — theorem BookProof.ChapterE4.cond_prob_sum
import Mathlib
import Definitions.Def_ChapterE4
open BookProof.ChapterE4


open scoped BigOperators

Formal statement

theorem BookProof.ChapterE4.cond_prob_sum (θ : ℕ → ℝ) (s : ℕ) :
    Real.cos (θ s) ^ 2 + Real.sin (θ s) ^ 2 = 1 := by sorry

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