`BookProof.ChapterCoherentOverlap.norm_sq_eq_sum` (q : EuclideanSpace ℝ (Fin n)) : ‖q‖ ^ 2 = ∑ i, q i * q i

Proved

BookProof.ChapterCoherentOverlap.norm_sq_eq_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOverlap.

BookProof.ChapterCoherentOverlap.norm_sq_eq_sum (q : EuclideanSpace ℝ (Fin n)) : ‖q‖ ^ 2 = ∑ i, q i * q i

Formalization note: Lean 4 identifier BookProof.ChapterCoherentOverlap.norm_sq_eq_sum.

Preamble

-- Generated from ChapterCoherentOverlap.lean — theorem BookProof.ChapterCoherentOverlap.norm_sq_eq_sum
import Mathlib
import Definitions.Def_ChapterCoherentOverlap
open BookProof.ChapterCoherentOverlap


open scoped BigOperators

noncomputable section


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterCoherentOverlap.norm_sq_eq_sum (q : EuclideanSpace ℝ (Fin n)) :
    ‖q‖ ^ 2 = ∑ i, q i * q i := by sorry

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