`BookProof.ChapterWignerLittleGroup.littleGroup_null_conj_SE2` (p : Fin 4 → ℝ) (hp0 : 0 < p 0) (hshell : p 0 ^ 2 - p 1 ^ 2 - p 2 ^ 2 - p 3 ^ 2 = 0) : ∃ A : Matrix (Fin 2) (Fin 2) ℂ

Proved

BookProof.ChapterWignerLittleGroup.littleGroup_null_conj_SE2

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWignerLittleGroup.

BookProof.ChapterWignerLittleGroup.littleGroup_null_conj_SE2 (p : Fin 4 → ℝ) (hp0 : 0 < p 0) (hshell : p 0 ^ 2 - p 1 ^ 2 - p 2 ^ 2 - p 3 ^ 2 = 0) : ∃ A : Matrix (Fin 2) (Fin 2) ℂ, A.det = 1 ∧ littleGroup p = (fun B => A * B * A⁻¹) '' SE2

Formalization note: Lean 4 identifier BookProof.ChapterWignerLittleGroup.littleGroup_null_conj_SE2.

Preamble

-- Generated from ChapterWignerLittleGroup.lean — theorem BookProof.ChapterWignerLittleGroup.littleGroup_null_conj_SE2
import Mathlib
import Definitions.Def_ChapterWignerLittleGroup
import Definitions.Def_ChapterLittleGroup
open BookProof.ChapterLittleGroup
open BookProof.ChapterWignerLittleGroup


open Matrix Complex

Formal statement

theorem BookProof.ChapterWignerLittleGroup.littleGroup_null_conj_SE2 (p : Fin 4 → ℝ) (hp0 : 0 < p 0)
    (hshell : p 0 ^ 2 - p 1 ^ 2 - p 2 ^ 2 - p 3 ^ 2 = 0) :
    ∃ A : Matrix (Fin 2) (Fin 2) ℂ, A.det = 1 ∧
      littleGroup p = (fun B => A * B * A⁻¹) '' SE2 := by sorry

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