`BookProof.ChapterWeylSl2.Sl2Rep.mem_scalarOps` {W : Submodule ℂ V} {f : Module.End ℂ V} : f ∈ scalarOps W ↔ (∀ v : V, f v ∈ W) ∧ ∃ c : ℂ, ∀ w ∈ W, f w = c • w

Proved

BookProof.ChapterWeylSl2.Sl2Rep.mem_scalarOps

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylSl2.

BookProof.ChapterWeylSl2.Sl2Rep.mem_scalarOps {W : Submodule ℂ V} {f : Module.End ℂ V} : f ∈ scalarOps W ↔ (∀ v : V, f v ∈ W) ∧ ∃ c : ℂ, ∀ w ∈ W, f w = c • w

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

Preamble

-- Generated from ChapterWeylSl2.lean — theorem BookProof.ChapterWeylSl2.Sl2Rep.mem_scalarOps
import Mathlib
import Definitions.Def_ChapterWeylSl2
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.mem_scalarOps {W : Submodule ℂ V} {f : Module.End ℂ V} :
    f ∈ scalarOps W ↔ (∀ v : V, f v ∈ W) ∧ ∃ c : ℂ, ∀ w ∈ W, f w = c • w := by sorry

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