`BookProof.ChapterA4f.no_tachyon` (p : Fin 3 → ℝ) (m₁ m₂ : ℝ) : energySymbolR p m₁ m₂ * energySymbolR p m₁ m₂ = ((p 0) ^ 2 + (p 1) ^ 2 + (p 2) ^ 2 - (m₁ ^ 2 + m₂ ^ 2)) •...

Proved

BookProof.ChapterA4f.no_tachyon

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4f.

BookProof.ChapterA4f.no_tachyon (p : Fin 3 → ℝ) (m₁ m₂ : ℝ) : energySymbolR p m₁ m₂ * energySymbolR p m₁ m₂ = ((p 0) ^ 2 + (p 1) ^ 2 + (p 2) ^ 2 - (m₁ ^ 2 + m₂ ^ 2)) • (1 : Matrix (Fin 4) (Fin 4) ℝ)

Formalization note: Lean 4 identifier BookProof.ChapterA4f.no_tachyon.

Preamble

-- Generated from ChapterA4f.lean — theorem BookProof.ChapterA4f.no_tachyon
import Definitions.Def_ChapterA3
import Mathlib
import Definitions.Def_ChapterA4f
import Definitions.Def_ChapterA5
open BookProof.ChapterA5
open BookProof.ChapterA4f


open Matrix
open scoped ComplexConjugate


open BookProof.ChapterA3 BookProof.ChapterA5

Formal statement

theorem BookProof.ChapterA4f.no_tachyon (p : Fin 3 → ℝ) (m₁ m₂ : ℝ) :
    energySymbolR p m₁ m₂ * energySymbolR p m₁ m₂
      = ((p 0) ^ 2 + (p 1) ^ 2 + (p 2) ^ 2 - (m₁ ^ 2 + m₂ ^ 2)) •
          (1 : Matrix (Fin 4) (Fin 4) ℝ) := by sorry

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