Prove2Me

`BookProof.ChapterA.Jmap_mem_JY` {Y : Submodule ℝ V} {y : V} (hy : y ∈ Y) : Jmap y ∈ JY Y

Proved
BookProof.ChapterA.Jmap_mem_JY

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1e.

BookProof.ChapterA.Jmap_mem_JY {Y : Submodule ℝ V} {y : V} (hy : y ∈ Y) : Jmap y ∈ JY Y

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

Preamble
-- Generated from ChapterA1e.lean — theorem BookProof.ChapterA.Jmap_mem_JY
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.Jmap_mem_JY {Y : Submodule ℝ V} {y : V} (hy : y ∈ Y) : Jmap y ∈ JY Y := by sorry

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