`BookProof.ChapterA5.energySymbolZ_sq` (p : Fin 3 → ℤ) (m₁ m₂ : ℤ) : energySymbolZ p m₁ m₂ * energySymbolZ p m₁ m₂ = ((p 0) ^ 2 + (p 1) ^ 2 + (p 2) ^ 2 - m₁ ^ 2 - m₂ ^ 2)...

Proved

BookProof.ChapterA5.energySymbolZ_sq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA5.

BookProof.ChapterA5.energySymbolZ_sq (p : Fin 3 → ℤ) (m₁ m₂ : ℤ) : energySymbolZ p m₁ m₂ * energySymbolZ p m₁ m₂ = ((p 0) ^ 2 + (p 1) ^ 2 + (p 2) ^ 2 - m₁ ^ 2 - m₂ ^ 2) • (1 : Matrix (Fin 4) (Fin 4) ℤ)

Formalization note: Lean 4 identifier BookProof.ChapterA5.energySymbolZ_sq.

Preamble

-- Generated from ChapterA5.lean — theorem BookProof.ChapterA5.energySymbolZ_sq
import Definitions.Def_ChapterA3
import Mathlib
import Definitions.Def_ChapterA5
open BookProof.ChapterA5


open Matrix


open BookProof.ChapterA3

Formal statement

theorem BookProof.ChapterA5.energySymbolZ_sq (p : Fin 3 → ℤ) (m₁ m₂ : ℤ) :
    energySymbolZ p m₁ m₂ * energySymbolZ p m₁ m₂
      = ((p 0) ^ 2 + (p 1) ^ 2 + (p 2) ^ 2 - m₁ ^ 2 - m₂ ^ 2) •
          (1 : Matrix (Fin 4) (Fin 4) ℤ) := by sorry

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