`BookProof.ChapterA4h.prop87_88_assembled` (Mk : MackeyImprimitivity R) (Wg : WignerClassification R Mk) (ρ : R) : (PoincareType.of (Mk.massSq ρ) (Mk.contSpin ρ) = PoincareType.mas

Proved

BookProof.ChapterA4h.prop87_88_assembled

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4h.

BookProof.ChapterA4h.prop87_88_assembled (Mk : MackeyImprimitivity R) (Wg : WignerClassification R Mk) (ρ : R) : (PoincareType.of (Mk.massSq ρ) (Mk.contSpin ρ) = PoincareType.massive ∨ PoincareType.of (Mk.massSq ρ) (Mk.contSpin ρ) = PoincareType.masslessDiscrete) ∧ ¬ ∀ j : Fin 3, projPos * spatialOp j = spatialOp j * projPos

Formalization note: Lean 4 identifier BookProof.ChapterA4h.prop87_88_assembled.

Preamble

-- Generated from ChapterA4h.lean — theorem BookProof.ChapterA4h.prop87_88_assembled
import Definitions.Def_ChapterA4f
import Definitions.Def_ChapterA5
import Mathlib
import Definitions.Def_ChapterA4h
import Definitions.Def_ChapterA4e
import Definitions.Def_ChapterWeylCauchyRiemann
open BookProof.ChapterA4e
open BookProof.WeylCauchyRiemann
open BookProof.ChapterA4h


open Matrix


open BookProof.ChapterA4e BookProof.ChapterA4f BookProof.ChapterA5

variable (R : Type*)

Formal statement

theorem BookProof.ChapterA4h.prop87_88_assembled (Mk : MackeyImprimitivity R)
    (Wg : WignerClassification R Mk) (ρ : R) :
    (PoincareType.of (Mk.massSq ρ) (Mk.contSpin ρ) = PoincareType.massive ∨
      PoincareType.of (Mk.massSq ρ) (Mk.contSpin ρ) = PoincareType.masslessDiscrete) ∧
    ¬ ∀ j : Fin 3, projPos * spatialOp j = spatialOp j * projPos := by sorry

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