`BookProof.ChapterEulerStochastic.exists_cos_sq` {p : ℝ} (hp0 : 0 ≤ p) (hp1 : p ≤ 1) : ∃ a : ℝ, Real.cos a ^ 2 = p

Proved

BookProof.ChapterEulerStochastic.exists_cos_sq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerStochastic.

BookProof.ChapterEulerStochastic.exists_cos_sq {p : ℝ} (hp0 : 0 ≤ p) (hp1 : p ≤ 1) : ∃ a : ℝ, Real.cos a ^ 2 = p

Formalization note: Lean 4 identifier BookProof.ChapterEulerStochastic.exists_cos_sq.

Preamble

-- Generated from ChapterEulerStochastic.lean — theorem BookProof.ChapterEulerStochastic.exists_cos_sq
import Mathlib
import Definitions.Def_ChapterEulerStochastic
open BookProof.ChapterEulerStochastic


open scoped Matrix BigOperators

Formal statement

theorem BookProof.ChapterEulerStochastic.exists_cos_sq {p : ℝ} (hp0 : 0 ≤ p) (hp1 : p ≤ 1) :
    ∃ a : ℝ, Real.cos a ^ 2 = p := by sorry

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