`BookProof.HermiteBandHigher.IsBandR.sum` {r m : ℕ} {ι : Type*} (s : Finset ι) (F : ι → MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ) (h : ∀ i ∈ s, IsBandR r m (F i))...

Proved

BookProof.HermiteBandHigher.IsBandR.sum

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteBandCalculusHigher.

BookProof.HermiteBandHigher.IsBandR.sum {r m : ℕ} {ι : Type*} (s : Finset ι) (F : ι → MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ) (h : ∀ i ∈ s, IsBandR r m (F i)) : IsBandR r m (∑ i ∈ s, F i)

Formalization note: Lean 4 identifier BookProof.HermiteBandHigher.IsBandR.sum.

Preamble

-- Generated from ChapterHermiteBandCalculusHigher.lean — theorem BookProof.HermiteBandHigher.IsBandR.sum
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterHermiteProductBasis
import Definitions.Def_ChapterHermiteBandCalculus
import Definitions.Def_ChapterYangMillsHermite
import Definitions.Def_ChapterNavierStokesDifferentialL2
import Mathlib
import Definitions.Def_ChapterHermiteBandCalculusHigher
import Definitions.Def_ChapterSirkFinitePrecision
open BookProof.SirkFinitePrecision
open BookProof.SirkFinitePrecision.CertInterval
open BookProof.HermiteBandHigher



noncomputable section

open MvPolynomial BookProof.HermiteProductCore BookProof.HermiteProductBasis
open BookProof.HermiteBand BookProof.YangMillsHermite
open BookProof.NavierStokesFlow.DifferentialL2

variable {d : ℕ}

Formal statement

theorem BookProof.HermiteBandHigher.IsBandR.sum {r m : ℕ} {ι : Type*} (s : Finset ι)
    (F : ι → MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ)
    (h : ∀ i ∈ s, IsBandR r m (F i)) : IsBandR r m (∑ i ∈ s, F i) := by sorry

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