`BookProof.ChapterMaschkeFiniteGroup.avgProj_eq_self` [Fintype G] {ρ : Representation ℂ G V} {W : Submodule ℂ V} (hW : IsInvariant ρ W) (pi : V →ₗ[ℂ] V) (hpi : ∀ x ∈ W, pi x = x) {
ProvedBookProof.ChapterMaschkeFiniteGroup.avgProj_eq_selftheoremstimepiece
Prove the following Lean 4 theorem from ChapterMaschkeFiniteGroup.
BookProof.ChapterMaschkeFiniteGroup.avgProj_eq_self [Fintype G] {ρ : Representation ℂ G V} {W : Submodule ℂ V} (hW : IsInvariant ρ W) (pi : V →ₗ[ℂ] V) (hpi : ∀ x ∈ W, pi x = x) {x : V} (hx : x ∈ W) : avgProj ρ pi x = x
Formalization note: Lean 4 identifier BookProof.ChapterMaschkeFiniteGroup.avgProj_eq_self.
Preamble
-- Generated from ChapterMaschkeFiniteGroup.lean — theorem BookProof.ChapterMaschkeFiniteGroup.avgProj_eq_self
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_eq_self [Fintype G] {ρ : Representation ℂ G V} {W : Submodule ℂ V}
(hW : IsInvariant ρ W) (pi : V →ₗ[ℂ] V) (hpi : ∀ x ∈ W, pi x = x) {x : V} (hx : x ∈ W) :
avgProj ρ pi x = x := by sorry