`BookProof.ChapterOrthogonalSums.hasSum_norm_sq_of_hasSum` {ι : Type*} {v : ι → E} {psi : E} (h : HasSum v psi) (horth : ∀ x y, x ≠ y → ⟪v x, v y⟫_ℂ = 0) : HasSum (fun x => ‖v x‖ ^

Proved

BookProof.ChapterOrthogonalSums.hasSum_norm_sq_of_hasSum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterOrthogonalSums.

BookProof.ChapterOrthogonalSums.hasSum_norm_sq_of_hasSum {ι : Type*} {v : ι → E} {psi : E} (h : HasSum v psi) (horth : ∀ x y, x ≠ y → ⟪v x, v y⟫_ℂ = 0) : HasSum (fun x => ‖v x‖ ^ 2) (‖psi‖ ^ 2)

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

Preamble

-- Generated from ChapterOrthogonalSums.lean — theorem BookProof.ChapterOrthogonalSums.hasSum_norm_sq_of_hasSum
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.hasSum_norm_sq_of_hasSum {ι : Type*} {v : ι → E} {psi : E} (h : HasSum v psi)
    (horth : ∀ x y, x ≠ y → ⟪v x, v y⟫_ℂ = 0) :
    HasSum (fun x => ‖v x‖ ^ 2) (‖psi‖ ^ 2) := by sorry

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