`BookProof.ChapterA4h.localizable_iff_massShell` (p : Fin 3 → ℝ) (m₁ m₂ : ℝ) : Localizable p m₁ m₂ ↔ p 0 ^ 2 + p 1 ^ 2 + p 2 ^ 2 = m₁ ^ 2 + m₂ ^ 2

Proved

BookProof.ChapterA4h.localizable_iff_massShell

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4h.

BookProof.ChapterA4h.localizable_iff_massShell (p : Fin 3 → ℝ) (m₁ m₂ : ℝ) : Localizable p m₁ m₂ ↔ p 0 ^ 2 + p 1 ^ 2 + p 2 ^ 2 = m₁ ^ 2 + m₂ ^ 2

Formalization note: Lean 4 identifier BookProof.ChapterA4h.localizable_iff_massShell.

Preamble

-- Generated from ChapterA4h.lean — theorem BookProof.ChapterA4h.localizable_iff_massShell
import Definitions.Def_ChapterA4e
import Definitions.Def_ChapterA4f
import Mathlib
import Definitions.Def_ChapterA4h
import Definitions.Def_ChapterA5
open BookProof.ChapterA5
open BookProof.ChapterA4h


open Matrix


open BookProof.ChapterA4e BookProof.ChapterA4f BookProof.ChapterA5

Formal statement

theorem BookProof.ChapterA4h.localizable_iff_massShell (p : Fin 3 → ℝ) (m₁ m₂ : ℝ) :
    Localizable p m₁ m₂ ↔ p 0 ^ 2 + p 1 ^ 2 + p 2 ^ 2 = m₁ ^ 2 + m₂ ^ 2 := by sorry

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