`BookProof.ChapterA.exists_unit_sqrt` (c : ℂ) (hc : ‖c‖ = 1) : ∃ l : ℂ, l ^ 2 = c ∧ ‖l‖ = 1

Proved

BookProof.ChapterA.exists_unit_sqrt

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2d.

BookProof.ChapterA.exists_unit_sqrt (c : ℂ) (hc : ‖c‖ = 1) : ∃ l : ℂ, l ^ 2 = c ∧ ‖l‖ = 1

Formalization note: Lean 4 identifier BookProof.ChapterA.exists_unit_sqrt.

Preamble

-- Generated from ChapterA2d.lean — theorem BookProof.ChapterA.exists_unit_sqrt
import Mathlib
import Definitions.Def_ChapterA2d
import Definitions.Def_ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace


variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]
variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℂ W] [CompleteSpace W]

Formal statement

theorem BookProof.ChapterA.exists_unit_sqrt (c : ℂ) (hc : ‖c‖ = 1) :
    ∃ l : ℂ, l ^ 2 = c ∧ ‖l‖ = 1 := by sorry

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