Prove2Me

`BookProof.Complexification.Cx.complexify_cxConj_invariant` (Y : Submodule ℝ W) : ∀ x ∈ complexify Y, cxConj x ∈ complexify Y

Proved
BookProof.Complexification.Cx.complexify_cxConj_invariant

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1b.

BookProof.Complexification.Cx.complexify_cxConj_invariant (Y : Submodule ℝ W) : ∀ x ∈ complexify Y, cxConj x ∈ complexify Y

Formalization note: Lean 4 identifier BookProof.Complexification.Cx.complexify_cxConj_invariant.

Preamble
-- Generated from ChapterA1b.lean — theorem BookProof.Complexification.Cx.complexify_cxConj_invariant
import Definitions.Def_ChapterA
import Mathlib
import Definitions.Def_ChapterA1b
import Definitions.Def_Complexification
open BookProof.Complexification
open BookProof.Complexification.Cx


open scoped RealInnerProductSpace
open BookProof.ChapterA


variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℝ W]
Formal statement
theorem BookProof.Complexification.Cx.complexify_cxConj_invariant (Y : Submodule ℝ W) :
    ∀ x ∈ complexify Y, cxConj x ∈ complexify Y := by sorry

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