`BookProof.NavierStokesFlow.Carleman.summable_mul_shift` (w : L2N) : Summable fun n : ℕ => ‖(w : ℕ → ℂ) n‖ * ‖(w : ℕ → ℂ) (n + 1)‖

Proved

BookProof.NavierStokesFlow.Carleman.summable_mul_shift

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesCarleman.

BookProof.NavierStokesFlow.Carleman.summable_mul_shift (w : L2N) : Summable fun n : ℕ => ‖(w : ℕ → ℂ) n‖ * ‖(w : ℕ → ℂ) (n + 1)‖

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.Carleman.summable_mul_shift.

Preamble

-- Generated from ChapterNavierStokesCarleman.lean — theorem BookProof.NavierStokesFlow.Carleman.summable_mul_shift
import Mathlib
import Definitions.Def_ChapterNavierStokesCarleman
import Definitions.Def_ChapterContinuityUnitaryInfinite
import Definitions.Def_ChapterNavierStokesDeficiency
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.ChapterContinuityUnitaryInfinite
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.JacobiDeficiency
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.Carleman


open scoped ENNReal



open LpNat DiagonalEsa FullEsa

Formal statement

theorem BookProof.NavierStokesFlow.Carleman.summable_mul_shift (w : L2N) :
    Summable fun n : ℕ => ‖(w : ℕ → ℂ) n‖ * ‖(w : ℕ → ℂ) (n + 1)‖ := by sorry

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