`BookProof.ChapterEll2Separable.sum_single_rat_mem_range` (s : Finset ℕ) (q : ℕ → ℚ) : (∑ i ∈ s, lp.single 2 i ((q i : ℝ))) ∈ Set.range ratVec

Proved

BookProof.ChapterEll2Separable.sum_single_rat_mem_range

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEll2Separable.

BookProof.ChapterEll2Separable.sum_single_rat_mem_range (s : Finset ℕ) (q : ℕ → ℚ) : (∑ i ∈ s, lp.single 2 i ((q i : ℝ))) ∈ Set.range ratVec

Formalization note: Lean 4 identifier BookProof.ChapterEll2Separable.sum_single_rat_mem_range.

Preamble

-- Generated from ChapterEll2Separable.lean — theorem BookProof.ChapterEll2Separable.sum_single_rat_mem_range
import Mathlib
import Definitions.Def_ChapterEll2Separable
import Definitions.Def_ChapterRieszFischer
open BookProof.ChapterRieszFischer
open BookProof.ChapterEll2Separable


open Filter Finset
open scoped ENNReal


open BookProof.ChapterRieszFischer

Formal statement

theorem BookProof.ChapterEll2Separable.sum_single_rat_mem_range (s : Finset ℕ) (q : ℕ → ℚ) :
    (∑ i ∈ s, lp.single 2 i ((q i : ℝ))) ∈ Set.range ratVec := by sorry

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