`BookProof.ChapterAbelianDiagonalCountable.diagOp_coordUnit_apply` (i : ℕ) (f : Ell2C) (j : ℕ) : ((diagOp (coordUnit i) f : Ell2C) : ℕ → ℂ) j = if j = i then (f : ℕ → ℂ) i else 0

Proved

BookProof.ChapterAbelianDiagonalCountable.diagOp_coordUnit_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianDiagonalCountable.

BookProof.ChapterAbelianDiagonalCountable.diagOp_coordUnit_apply (i : ℕ) (f : Ell2C) (j : ℕ) : ((diagOp (coordUnit i) f : Ell2C) : ℕ → ℂ) j = if j = i then (f : ℕ → ℂ) i else 0

Formalization note: Lean 4 identifier BookProof.ChapterAbelianDiagonalCountable.diagOp_coordUnit_apply.

Preamble

-- Generated from ChapterAbelianDiagonalCountable.lean — theorem BookProof.ChapterAbelianDiagonalCountable.diagOp_coordUnit_apply
import Mathlib
import Definitions.Def_ChapterAbelianDiagonalCountable
open BookProof.ChapterAbelianDiagonalCountable


open scoped ENNReal

noncomputable section

Formal statement

theorem BookProof.ChapterAbelianDiagonalCountable.diagOp_coordUnit_apply (i : ℕ) (f : Ell2C) (j : ℕ) :
    ((diagOp (coordUnit i) f : Ell2C) : ℕ → ℂ) j = if j = i then (f : ℕ → ℂ) i else 0 := by sorry

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