`BookProof.ChapterE.cos_sq_surjective` {p : ℝ} (hp0 : 0 ≤ p) (hp1 : p ≤ 1) : ∃ t : ℝ, Real.cos t ^ 2 = p

Proved

BookProof.ChapterE.cos_sq_surjective

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterE.

BookProof.ChapterE.cos_sq_surjective {p : ℝ} (hp0 : 0 ≤ p) (hp1 : p ≤ 1) : ∃ t : ℝ, Real.cos t ^ 2 = p

Formalization note: Lean 4 identifier BookProof.ChapterE.cos_sq_surjective.

Preamble

-- Generated from ChapterE.lean — theorem BookProof.ChapterE.cos_sq_surjective
import Mathlib
import Definitions.Def_ChapterE
open BookProof.ChapterE


open scoped Matrix BigOperators
open Filter
open scoped Topology

Formal statement

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

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