`BookProof.ChapterMaschkeFiniteGroup.avgProj_apply` [Fintype G] (ρ : Representation ℂ G V) (pi : V →ₗ[ℂ] V) (x : V) : avgProj ρ pi x = (Fintype.card G : ℂ)⁻¹ • ∑ g : G, ρ g (pi (ρ

Proved

BookProof.ChapterMaschkeFiniteGroup.avgProj_apply

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMaschkeFiniteGroup.

BookProof.ChapterMaschkeFiniteGroup.avgProj_apply [Fintype G] (ρ : Representation ℂ G V) (pi : V →ₗ[ℂ] V) (x : V) : avgProj ρ pi x = (Fintype.card G : ℂ)⁻¹ • ∑ g : G, ρ g (pi (ρ g⁻¹ x))

Formalization note: Lean 4 identifier BookProof.ChapterMaschkeFiniteGroup.avgProj_apply.

Preamble

-- Generated from ChapterMaschkeFiniteGroup.lean — theorem BookProof.ChapterMaschkeFiniteGroup.avgProj_apply
import Mathlib
import Definitions.Def_ChapterMaschkeFiniteGroup
open BookProof.ChapterMaschkeFiniteGroup



variable {G : Type*} [Group G] {V : Type*} [AddCommGroup V] [Module ℂ V]

Formal statement

theorem BookProof.ChapterMaschkeFiniteGroup.avgProj_apply [Fintype G] (ρ : Representation ℂ G V) (pi : V →ₗ[ℂ] V) (x : V) :
    avgProj ρ pi x = (Fintype.card G : ℂ)⁻¹ • ∑ g : G, ρ g (pi (ρ g⁻¹ x)) := by sorry

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