`BookProof.ChapterWeylSL2Group.rho_mem_of_isInv` (h : IsExpOfSl2 rho R N) {W : Submodule ℂ V} (hW : R.IsInv W) : ∀ t : ℂ, (∀ v ∈ W, rho (uPlus t) v ∈ W) ∧ (∀ v ∈ W, rho (uMinus t)

Proved

BookProof.ChapterWeylSL2Group.rho_mem_of_isInv

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylSL2Group.

BookProof.ChapterWeylSL2Group.rho_mem_of_isInv (h : IsExpOfSl2 rho R N) {W : Submodule ℂ V} (hW : R.IsInv W) : ∀ t : ℂ, (∀ v ∈ W, rho (uPlus t) v ∈ W) ∧ (∀ v ∈ W, rho (uMinus t) v ∈ W)

Formalization note: Lean 4 identifier BookProof.ChapterWeylSL2Group.rho_mem_of_isInv.

Preamble

-- Generated from ChapterWeylSL2Group.lean — theorem BookProof.ChapterWeylSL2Group.rho_mem_of_isInv
import Mathlib
import Definitions.Def_ChapterWeylSL2Group
import Definitions.Def_ChapterDoubleSlit
import Definitions.Def_ChapterGleasonPureMixed
import Definitions.Def_ChapterWeylSl2
open BookProof.ChapterDoubleSlit
open BookProof.ChapterGleasonPureMixed
open BookProof.ChapterWeylSl2
open BookProof.ChapterWeylSl2
open BookProof.ChapterWeylSL2Group



open BookProof.ChapterWeylSl2

universe u

variable {V : Type u} [AddCommGroup V] [Module ℂ V]

variable {rho : Representation ℂ (Matrix.SpecialLinearGroup (Fin 2) ℂ) V} {R : Sl2Rep V} {N : ℕ}

Formal statement

theorem BookProof.ChapterWeylSL2Group.rho_mem_of_isInv (h : IsExpOfSl2 rho R N) {W : Submodule ℂ V} (hW : R.IsInv W) :
    ∀ t : ℂ, (∀ v ∈ W, rho (uPlus t) v ∈ W) ∧ (∀ v ∈ W, rho (uMinus t) v ∈ W) := by sorry

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