`BookProof.ChapterAbelianAtomicCondensation.atomProj_apply` (i : ℕ) (f : Ell2C) : atomProj i f = (f : ℕ → ℂ) i • atom i

Proved

BookProof.ChapterAbelianAtomicCondensation.atomProj_apply

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianAtomicCondensation.

BookProof.ChapterAbelianAtomicCondensation.atomProj_apply (i : ℕ) (f : Ell2C) : atomProj i f = (f : ℕ → ℂ) i • atom i

Formalization note: Lean 4 identifier BookProof.ChapterAbelianAtomicCondensation.atomProj_apply.

Preamble

-- Generated from ChapterAbelianAtomicCondensation.lean — theorem BookProof.ChapterAbelianAtomicCondensation.atomProj_apply
import Mathlib
import Definitions.Def_ChapterAbelianAtomicCondensation
import Definitions.Def_ChapterAbelianDiagonalCountable
open BookProof.ChapterAbelianDiagonalCountable
open BookProof.ChapterAbelianAtomicCondensation


open scoped ENNReal

noncomputable section


open BookProof.ChapterAbelianDiagonalCountable

Formal statement

theorem BookProof.ChapterAbelianAtomicCondensation.atomProj_apply (i : ℕ) (f : Ell2C) : atomProj i f = (f : ℕ → ℂ) i • atom i := by sorry

View graph