Prove2Me

`BookProof.Complexification.Cx.cxConj_inner` (x y : Cx W) : inner ℂ (cxConj x) (cxConj y) = starRingEnd ℂ (inner ℂ x y)

Proved
BookProof.Complexification.Cx.cxConj_inner

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

theoremstimepiece

Prove the following Lean 4 theorem from Complexification.

BookProof.Complexification.Cx.cxConj_inner (x y : Cx W) : inner ℂ (cxConj x) (cxConj y) = starRingEnd ℂ (inner ℂ x y)

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

Preamble
-- Generated from Complexification.lean — theorem BookProof.Complexification.Cx.cxConj_inner
import Mathlib
import Definitions.Def_Complexification
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_inner (x y : Cx W) :
    inner ℂ (cxConj x) (cxConj y) = starRingEnd ℂ (inner ℂ x y) := by sorry

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