Prove2Me

`BookProof.ChapterSchurRepresentation.imprimitivitySystem_isNormal` {G : Type*} [Group G] {X : Type*} (U : G →* (V ≃ₗᵢ[ℂ] V)) (pvm : Set X → (V →L[ℂ] V)) (hpvm : ∀ A : Set X, IsSel

Proved
BookProof.ChapterSchurRepresentation.imprimitivitySystem_isNormal

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSchurRepresentation.

BookProof.ChapterSchurRepresentation.imprimitivitySystem_isNormal {G : Type*} [Group G] {X : Type*} (U : G →* (V ≃ₗᵢ[ℂ] V)) (pvm : Set X → (V →L[ℂ] V)) (hpvm : ∀ A : Set X, IsSelfAdjoint (pvm A)) : (imprimitivitySystem U pvm).IsNormal

Formalization note: Lean 4 identifier BookProof.ChapterSchurRepresentation.imprimitivitySystem_isNormal.

Preamble
-- Generated from ChapterSchurRepresentation.lean — theorem BookProof.ChapterSchurRepresentation.imprimitivitySystem_isNormal
import Definitions.Def_ChapterSchurIrreducible
import Mathlib
import Definitions.Def_ChapterSchurRepresentation
import Definitions.Def_ChapterA
open BookProof.ChapterA
open BookProof.ChapterA.System
open BookProof.ChapterSchurRepresentation


open scoped ComplexConjugate InnerProductSpace


open BookProof.ChapterA BookProof.ChapterA.System BookProof.ChapterSchurIrreducible

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]
Formal statement
theorem BookProof.ChapterSchurRepresentation.imprimitivitySystem_isNormal {G : Type*} [Group G] {X : Type*}
    (U : G →* (V ≃ₗᵢ[ℂ] V)) (pvm : Set X → (V →L[ℂ] V))
    (hpvm : ∀ A : Set X, IsSelfAdjoint (pvm A)) :
    (imprimitivitySystem U pvm).IsNormal := by sorry

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