`BookProof.ChapterA.JY_isClosed` {Y : Submodule ℝ V} (hY : IsClosed (Y : Set V)) : IsClosed ((JY Y : Submodule ℝ V) : Set V)

Proved

BookProof.ChapterA.JY_isClosed

by leonardopedro · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1e.

BookProof.ChapterA.JY_isClosed {Y : Submodule ℝ V} (hY : IsClosed (Y : Set V)) : IsClosed ((JY Y : Submodule ℝ V) : Set V)

Formalization note: Lean 4 identifier BookProof.ChapterA.JY_isClosed.

Preamble

-- Generated from ChapterA1e.lean — theorem BookProof.ChapterA.JY_isClosed
import Mathlib
import Definitions.Def_ChapterA1e
import Definitions.Def_ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace RealInnerProductSpace


attribute [local instance] InnerProductSpace.rclikeToReal

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]

Formal statement

theorem BookProof.ChapterA.JY_isClosed {Y : Submodule ℝ V} (hY : IsClosed (Y : Set V)) :
    IsClosed ((JY Y : Submodule ℝ V) : Set V) := by sorry

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