Prove2Me

`BookProof.ChapterNumericalRangeCrouzeix.inner_self_re` (x : E) : (⟪x, x⟫_ℂ).re = ‖x‖ ^ 2

Proved
BookProof.ChapterNumericalRangeCrouzeix.inner_self_re

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNumericalRangeCrouzeix.

BookProof.ChapterNumericalRangeCrouzeix.inner_self_re (x : E) : (⟪x, x⟫_ℂ).re = ‖x‖ ^ 2

Formalization note: Lean 4 identifier BookProof.ChapterNumericalRangeCrouzeix.inner_self_re.

Preamble
-- Generated from ChapterNumericalRangeCrouzeix.lean — theorem BookProof.ChapterNumericalRangeCrouzeix.inner_self_re
import Mathlib
import Definitions.Def_ChapterNumericalRangeCrouzeix
open BookProof.ChapterNumericalRangeCrouzeix


open scoped InnerProductSpace


variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E]
Formal statement
theorem BookProof.ChapterNumericalRangeCrouzeix.inner_self_re (x : E) : (⟪x, x⟫_ℂ).re = ‖x‖ ^ 2 := by sorry

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