`BookProof.ChapterDisplacedThermalMulti.norm_sq_eq_sum` (a b : EuclideanSpace ℝ (Fin n)) : ‖a - b‖ ^ 2 = ∑ i, (a i - b i) ^ 2

Proved

BookProof.ChapterDisplacedThermalMulti.norm_sq_eq_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDisplacedThermalMulti.

BookProof.ChapterDisplacedThermalMulti.norm_sq_eq_sum (a b : EuclideanSpace ℝ (Fin n)) : ‖a - b‖ ^ 2 = ∑ i, (a i - b i) ^ 2

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

Preamble

-- Generated from ChapterDisplacedThermalMulti.lean — theorem BookProof.ChapterDisplacedThermalMulti.norm_sq_eq_sum
import Definitions.Def_ChapterDisplacedThermalOverlap
import Mathlib
import Definitions.Def_ChapterDisplacedThermalMulti
open BookProof.ChapterDisplacedThermalMulti


noncomputable section

open MeasureTheory ProbabilityTheory Real
open scoped NNReal


open BookProof.ChapterDisplacedThermalOverlap

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterDisplacedThermalMulti.norm_sq_eq_sum (a b : EuclideanSpace ℝ (Fin n)) :
    ‖a - b‖ ^ 2 = ∑ i, (a i - b i) ^ 2 := by sorry

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