`BookProof.ChapterA.cembed_apply` (c : ℂ) (x : V) : (cembed c : V →L[ℝ] V) x = c • x

Proved

BookProof.ChapterA.cembed_apply

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2c.

BookProof.ChapterA.cembed_apply (c : ℂ) (x : V) : (cembed c : V →L[ℝ] V) x = c • x

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

Preamble

-- Generated from ChapterA2c.lean — theorem BookProof.ChapterA.cembed_apply
import Mathlib
import Definitions.Def_ChapterA2c
import Definitions.Def_ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace Quaternion


variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]

Formal statement

theorem BookProof.ChapterA.cembed_apply (c : ℂ) (x : V) : (cembed c : V →L[ℝ] V) x = c • x := by sorry

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