`BookProof.ChapterWeylSl2.Sl2Rep.highestWeight_nat` [FiniteDimensional ℂ V] {R : Sl2Rep V} {w : V} {lam : ℂ} (hw : w ≠ 0) (hE : R.E w = 0) (h : R.H w = lam • w) : ∃ m : ℕ, lam = (m

Proved

BookProof.ChapterWeylSl2.Sl2Rep.highestWeight_nat

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylSl2.

BookProof.ChapterWeylSl2.Sl2Rep.highestWeight_nat [FiniteDimensional ℂ V] {R : Sl2Rep V} {w : V} {lam : ℂ} (hw : w ≠ 0) (hE : R.E w = 0) (h : R.H w = lam • w) : ∃ m : ℕ, lam = (m : ℂ) ∧ (R.F ^ (m + 1)) w = 0

Formalization note: Lean 4 identifier BookProof.ChapterWeylSl2.Sl2Rep.highestWeight_nat.

Preamble

-- Generated from ChapterWeylSl2.lean — theorem BookProof.ChapterWeylSl2.Sl2Rep.highestWeight_nat
import Mathlib
import Definitions.Def_ChapterWeylSl2
import Definitions.Def_ChapterDoubleSlit
import Definitions.Def_ChapterGleasonPureMixed
open BookProof.ChapterDoubleSlit
open BookProof.ChapterGleasonPureMixed
open BookProof.ChapterWeylSl2
open BookProof.ChapterWeylSl2



universe u

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

variable (R : Sl2Rep V)
variable {R}
variable {R : Sl2Rep V}

Formal statement

theorem BookProof.ChapterWeylSl2.Sl2Rep.highestWeight_nat [FiniteDimensional ℂ V] {R : Sl2Rep V} {w : V} {lam : ℂ}
    (hw : w ≠ 0) (hE : R.E w = 0) (h : R.H w = lam • w) :
    ∃ m : ℕ, lam = (m : ℂ) ∧ (R.F ^ (m + 1)) w = 0 := by sorry

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