`BookProof.ChapterWeylSl2.Sl2Rep.ops_zero_of_trivial` {W : Submodule ℂ V} (hmaps : ∀ v : V, R.E v ∈ W ∧ R.F v ∈ W ∧ R.H v ∈ W) (hzero : ∀ x ∈ W, R.E x = 0 ∧ R.F x = 0 ∧ R.H...

Proved

BookProof.ChapterWeylSl2.Sl2Rep.ops_zero_of_trivial

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylSl2.

BookProof.ChapterWeylSl2.Sl2Rep.ops_zero_of_trivial {W : Submodule ℂ V} (hmaps : ∀ v : V, R.E v ∈ W ∧ R.F v ∈ W ∧ R.H v ∈ W) (hzero : ∀ x ∈ W, R.E x = 0 ∧ R.F x = 0 ∧ R.H x = 0) (v : V) : R.E v = 0 ∧ R.F v = 0 ∧ R.H v = 0

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

Preamble

-- Generated from ChapterWeylSl2.lean — theorem BookProof.ChapterWeylSl2.Sl2Rep.ops_zero_of_trivial
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.ops_zero_of_trivial {W : Submodule ℂ V}
    (hmaps : ∀ v : V, R.E v ∈ W ∧ R.F v ∈ W ∧ R.H v ∈ W)
    (hzero : ∀ x ∈ W, R.E x = 0 ∧ R.F x = 0 ∧ R.H x = 0) (v : V) :
    R.E v = 0 ∧ R.F v = 0 ∧ R.H v = 0 := by sorry

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