`BookProof.ChapterOrthogonalSums.summable_of_orthogonal_of_summable_norm_sq` [CompleteSpace E] {ι : Type*} {v : ι → E} (horth : ∀ x y, x ≠ y → ⟪v x, v y⟫_ℂ = 0) (hsum : Summable fu

Proved

BookProof.ChapterOrthogonalSums.summable_of_orthogonal_of_summable_norm_sq

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterOrthogonalSums.

BookProof.ChapterOrthogonalSums.summable_of_orthogonal_of_summable_norm_sq [CompleteSpace E] {ι : Type*} {v : ι → E} (horth : ∀ x y, x ≠ y → ⟪v x, v y⟫_ℂ = 0) (hsum : Summable fun x => ‖v x‖ ^ 2) : Summable v

Formalization note: Lean 4 identifier BookProof.ChapterOrthogonalSums.summable_of_orthogonal_of_summable_norm_sq.

Preamble

-- Generated from ChapterOrthogonalSums.lean — theorem BookProof.ChapterOrthogonalSums.summable_of_orthogonal_of_summable_norm_sq
import Mathlib
import Definitions.Def_ChapterOrthogonalSums
open BookProof.ChapterOrthogonalSums


open scoped InnerProductSpace


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

Formal statement

theorem BookProof.ChapterOrthogonalSums.summable_of_orthogonal_of_summable_norm_sq [CompleteSpace E] {ι : Type*} {v : ι → E}
    (horth : ∀ x y, x ≠ y → ⟪v x, v y⟫_ℂ = 0) (hsum : Summable fun x => ‖v x‖ ^ 2) :
    Summable v := by sorry

View graph