`BookProof.ChapterF3.projOnto_eq_starProjection` {ψ : E} (hψ : ‖ψ‖ = 1) (s : E) : projOnto ψ s = (Submodule.span ℂ {ψ}).starProjection s

Proved

BookProof.ChapterF3.projOnto_eq_starProjection

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF3.

BookProof.ChapterF3.projOnto_eq_starProjection {ψ : E} (hψ : ‖ψ‖ = 1) (s : E) : projOnto ψ s = (Submodule.span ℂ {ψ}).starProjection s

Formalization note: Lean 4 identifier BookProof.ChapterF3.projOnto_eq_starProjection.

Preamble

-- Generated from ChapterF3.lean — theorem BookProof.ChapterF3.projOnto_eq_starProjection
import Mathlib
import Definitions.Def_ChapterF3
open BookProof.ChapterF3


open scoped BigOperators
open Polynomial


noncomputable section

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E]

Formal statement

theorem BookProof.ChapterF3.projOnto_eq_starProjection {ψ : E} (hψ : ‖ψ‖ = 1) (s : E) :
    projOnto ψ s = (Submodule.span ℂ {ψ}).starProjection s := by sorry

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