`BookProof.Complexification.Cx.cxConj_fixed_iff` (x : Cx W) : cxConj x = x ↔ x.im = 0

Proved

BookProof.Complexification.Cx.cxConj_fixed_iff

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from Complexification.

BookProof.Complexification.Cx.cxConj_fixed_iff (x : Cx W) : cxConj x = x ↔ x.im = 0

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

Preamble

-- Generated from Complexification.lean — theorem BookProof.Complexification.Cx.cxConj_fixed_iff
import Mathlib
import Definitions.Def_Complexification
import Definitions.Def_ChapterQgOuterFockCoreFL
open BookProof.QgOuterFockCoreFL
open BookProof.QgOuterFockCoreFL.CoreData
open BookProof.Complexification
open BookProof.Complexification


open scoped RealInnerProductSpace
open RCLike


set_option linter.unusedSectionVars false

variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℝ W]

Formal statement

theorem BookProof.Complexification.Cx.cxConj_fixed_iff (x : Cx W) : cxConj x = x ↔ x.im = 0 := by sorry

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