`BookProof.ChapterE.exists_uniformizer` (n : ℕ) (hn : 1 ≤ n) : ∃ U : Matrix (Fin n) (Fin n) ℂ, Uᴴ * U = 1 ∧ ∀ i j, ‖U i j‖ ^ 2 = 1 / n

Proved

BookProof.ChapterE.exists_uniformizer

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterE.

BookProof.ChapterE.exists_uniformizer (n : ℕ) (hn : 1 ≤ n) : ∃ U : Matrix (Fin n) (Fin n) ℂ, Uᴴ * U = 1 ∧ ∀ i j, ‖U i j‖ ^ 2 = 1 / n

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

Preamble

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


open scoped Matrix BigOperators
open Filter
open scoped Topology

Formal statement

theorem BookProof.ChapterE.exists_uniformizer (n : ℕ) (hn : 1 ≤ n) :
    ∃ U : Matrix (Fin n) (Fin n) ℂ, Uᴴ * U = 1 ∧ ∀ i j, ‖U i j‖ ^ 2 = 1 / n := by sorry

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