Prove2Me

`BookProof.ChapterA.inf_JY_Jinvariant` (Y : Submodule ℝ V) : ∀ x ∈ Y ⊓ JY Y, Jmap x ∈ Y ⊓ JY Y

Proved
BookProof.ChapterA.inf_JY_Jinvariant

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1e.

BookProof.ChapterA.inf_JY_Jinvariant (Y : Submodule ℝ V) : ∀ x ∈ Y ⊓ JY Y, Jmap x ∈ Y ⊓ JY Y

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

Preamble
-- Generated from ChapterA1e.lean — theorem BookProof.ChapterA.inf_JY_Jinvariant
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.inf_JY_Jinvariant (Y : Submodule ℝ V) :
    ∀ x ∈ Y ⊓ JY Y, Jmap x ∈ Y ⊓ JY Y := by sorry

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