`BookProof.ChapterWignerLittleGroupOrbits.act_inv_of_act` {A X Y : Matrix (Fin 2) (Fin 2) ℂ} (hA : A.det = 1) (h : act A X = Y) : act A⁻¹ Y = X

Proved

BookProof.ChapterWignerLittleGroupOrbits.act_inv_of_act

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWignerLittleGroupOrbits.

BookProof.ChapterWignerLittleGroupOrbits.act_inv_of_act {A X Y : Matrix (Fin 2) (Fin 2) ℂ} (hA : A.det = 1) (h : act A X = Y) : act A⁻¹ Y = X

Formalization note: Lean 4 identifier BookProof.ChapterWignerLittleGroupOrbits.act_inv_of_act.

Preamble

-- Generated from ChapterWignerLittleGroupOrbits.lean — theorem BookProof.ChapterWignerLittleGroupOrbits.act_inv_of_act
import Mathlib
import Definitions.Def_ChapterWignerLittleGroupOrbits
import Definitions.Def_ChapterWignerLittleGroup
open BookProof.ChapterWignerLittleGroup
open BookProof.ChapterWignerLittleGroupOrbits


open Matrix Complex
open scoped ComplexOrder


open BookProof.ChapterWignerLittleGroup

Formal statement

theorem BookProof.ChapterWignerLittleGroupOrbits.act_inv_of_act {A X Y : Matrix (Fin 2) (Fin 2) ℂ} (hA : A.det = 1) (h : act A X = Y) :
    act A⁻¹ Y = X := by sorry

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