`BookProof.NavierStokesFlow.HermiteFarisLavine.hasSum_commForm` (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) : HasSum (fun n => 8 * κ * (amp κ n * ((starRingEnd ℂ) (((x : L2I ℕ) : ℕ → ℂ

Proved

BookProof.NavierStokesFlow.HermiteFarisLavine.hasSum_commForm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesHermiteFarisLavine.

BookProof.NavierStokesFlow.HermiteFarisLavine.hasSum_commForm (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) : HasSum (fun n => 8 * κ * (amp κ n * ((starRingEnd ℂ) (((x : L2I ℕ) : ℕ → ℂ) n) * ((x : L2I ℕ) : ℕ → ℂ) (n + 2)).re)) (commForm (nsH κ hκ) (diagMax (oscSymbol κ)) x)

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.HermiteFarisLavine.hasSum_commForm.

Preamble

-- Generated from ChapterNavierStokesHermiteFarisLavine.lean — theorem BookProof.NavierStokesFlow.HermiteFarisLavine.hasSum_commForm
import Mathlib
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.HermiteFarisLavine


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato

variable {κ : ℝ}
variable {x : maxDom (oscSymbol κ)}

Formal statement

theorem BookProof.NavierStokesFlow.HermiteFarisLavine.hasSum_commForm (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) :
    HasSum (fun n => 8 * κ * (amp κ n
        * ((starRingEnd ℂ) (((x : L2I ℕ) : ℕ → ℂ) n) * ((x : L2I ℕ) : ℕ → ℂ) (n + 2)).re))
      (commForm (nsH κ hκ) (diagMax (oscSymbol κ)) x) := by sorry

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