`BookProof.NavierStokesFlow.Carleman.sum_normSq_le` (c w : ℕ → ℂ) (hrec : ∀ n, tridiagFun c w n = Complex.I * w n) (N : ℕ) : ∑ n ∈ Finset.range (N + 1), ‖w n‖ ^ 2 ≤ ‖c N‖...

Proved

BookProof.NavierStokesFlow.Carleman.sum_normSq_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesCarleman.

BookProof.NavierStokesFlow.Carleman.sum_normSq_le (c w : ℕ → ℂ) (hrec : ∀ n, tridiagFun c w n = Complex.I * w n) (N : ℕ) : ∑ n ∈ Finset.range (N + 1), ‖w n‖ ^ 2 ≤ ‖c N‖ * (‖w (N + 1)‖ * ‖w N‖)

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

Preamble

-- Generated from ChapterNavierStokesCarleman.lean — theorem BookProof.NavierStokesFlow.Carleman.sum_normSq_le
import Mathlib
import Definitions.Def_ChapterNavierStokesCarleman
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.Carleman


open scoped ENNReal



open LpNat DiagonalEsa FullEsa

Formal statement

theorem BookProof.NavierStokesFlow.Carleman.sum_normSq_le (c w : ℕ → ℂ) (hrec : ∀ n, tridiagFun c w n = Complex.I * w n) (N : ℕ) :
    ∑ n ∈ Finset.range (N + 1), ‖w n‖ ^ 2 ≤ ‖c N‖ * (‖w (N + 1)‖ * ‖w N‖) := by sorry

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