`BookProof.NavierStokesFlow.HermiteFarisLavine.hasSum_inner_nsH_left` (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) (y : L2I ℕ) : HasSum (fun n => -Complex.I * crossA κ ((x : L2I ℕ) : ℕ

Proved

BookProof.NavierStokesFlow.HermiteFarisLavine.hasSum_inner_nsH_left

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesHermiteFarisLavine.

BookProof.NavierStokesFlow.HermiteFarisLavine.hasSum_inner_nsH_left (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) (y : L2I ℕ) : HasSum (fun n => -Complex.I * crossA κ ((x : L2I ℕ) : ℕ → ℂ) ((y : ℕ → ℂ)) n + Complex.I * crossB κ ((x : L2I ℕ) : ℕ → ℂ) ((y : ℕ → ℂ)) n) (inner ℂ (nsH κ hκ x : L2I ℕ) y)

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

Preamble

-- Generated from ChapterNavierStokesHermiteFarisLavine.lean — theorem BookProof.NavierStokesFlow.HermiteFarisLavine.hasSum_inner_nsH_left
import Mathlib
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterContinuityUnitaryInfinite
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.ChapterContinuityUnitaryInfinite
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_inner_nsH_left (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) (y : L2I ℕ) :
    HasSum (fun n => -Complex.I * crossA κ ((x : L2I ℕ) : ℕ → ℂ) ((y : ℕ → ℂ)) n
        + Complex.I * crossB κ ((x : L2I ℕ) : ℕ → ℂ) ((y : ℕ → ℂ)) n)
      (inner ℂ (nsH κ hκ x : L2I ℕ) y) := by sorry

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