`BookProof.ChapterUnitaryCompleteReducibility.unitary_complete_reducibility` [FiniteDimensional ℂ V] {ρ : G →* (V ≃ₗᵢ[ℂ] V)} {W : Submodule ℂ V} (hW : IsInvariant ρ W) : ∃ W' : Sub

Proved

BookProof.ChapterUnitaryCompleteReducibility.unitary_complete_reducibility

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterUnitaryCompleteReducibility.

BookProof.ChapterUnitaryCompleteReducibility.unitary_complete_reducibility [FiniteDimensional ℂ V] {ρ : G →* (V ≃ₗᵢ[ℂ] V)} {W : Submodule ℂ V} (hW : IsInvariant ρ W) : ∃ W' : Submodule ℂ V, IsInvariant ρ W' ∧ IsCompl W W'

Formalization note: Lean 4 identifier BookProof.ChapterUnitaryCompleteReducibility.unitary_complete_reducibility.

Preamble

-- Generated from ChapterUnitaryCompleteReducibility.lean — theorem BookProof.ChapterUnitaryCompleteReducibility.unitary_complete_reducibility
import Mathlib
import Definitions.Def_ChapterUnitaryCompleteReducibility
import Definitions.Def_ChapterMaschkeFiniteGroup
open BookProof.ChapterMaschkeFiniteGroup
open BookProof.ChapterUnitaryCompleteReducibility



open Submodule

variable {G : Type*} [Group G] {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V]

Formal statement

theorem BookProof.ChapterUnitaryCompleteReducibility.unitary_complete_reducibility [FiniteDimensional ℂ V]
    {ρ : G →* (V ≃ₗᵢ[ℂ] V)} {W : Submodule ℂ V} (hW : IsInvariant ρ W) :
    ∃ W' : Submodule ℂ V, IsInvariant ρ W' ∧ IsCompl W W' := by sorry

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