`BookProof.ChapterWeylSl2.Sl2Rep.isInv_scalarOps` {R : Sl2Rep V} {W : Submodule ℂ V} (hW : R.IsInv W) : (adRep R).IsInv (scalarOps W)

Proved

BookProof.ChapterWeylSl2.Sl2Rep.isInv_scalarOps

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylSl2.

BookProof.ChapterWeylSl2.Sl2Rep.isInv_scalarOps {R : Sl2Rep V} {W : Submodule ℂ V} (hW : R.IsInv W) : (adRep R).IsInv (scalarOps W)

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

Preamble

-- Generated from ChapterWeylSl2.lean — theorem BookProof.ChapterWeylSl2.Sl2Rep.isInv_scalarOps
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.isInv_scalarOps {R : Sl2Rep V} {W : Submodule ℂ V} (hW : R.IsInv W) :
    (adRep R).IsInv (scalarOps W) := by sorry

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