`BookProof.ChapterEulerNState.euler_wave_unit` (θ : ℕ → ℝ) {n : ℕ} (hn : 1 ≤ n) : ∑ k ∈ Finset.range n, (eulerWave θ n k) ^ 2 = 1

Proved

BookProof.ChapterEulerNState.euler_wave_unit

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerNState.

BookProof.ChapterEulerNState.euler_wave_unit (θ : ℕ → ℝ) {n : ℕ} (hn : 1 ≤ n) : ∑ k ∈ Finset.range n, (eulerWave θ n k) ^ 2 = 1

Formalization note: Lean 4 identifier BookProof.ChapterEulerNState.euler_wave_unit.

Preamble

-- Generated from ChapterEulerNState.lean — theorem BookProof.ChapterEulerNState.euler_wave_unit
import Mathlib
import Definitions.Def_ChapterEulerNState
import Definitions.Def_ChapterDoubleSlit
open BookProof.ChapterDoubleSlit
open BookProof.ChapterEulerNState


open scoped BigOperators

Formal statement

theorem BookProof.ChapterEulerNState.euler_wave_unit (θ : ℕ → ℝ) {n : ℕ} (hn : 1 ≤ n) :
    ∑ k ∈ Finset.range n, (eulerWave θ n k) ^ 2 = 1 := by sorry

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