`BookProof.HermiteBandHigher.Band.monoG` {T : MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ} {r M : ℕ} {C : ℝ} {g g' : ℕ → ℝ} (hC : 0 ≤ C) (hg : ∀ n, g n ≤ g' n)...

Proved

BookProof.HermiteBandHigher.Band.monoG

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteBandCalculusHigher.

BookProof.HermiteBandHigher.Band.monoG {T : MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ} {r M : ℕ} {C : ℝ} {g g' : ℕ → ℝ} (hC : 0 ≤ C) (hg : ∀ n, g n ≤ g' n) (h : Band T r M C g) : Band T r M C g'

Formalization note: Lean 4 identifier BookProof.HermiteBandHigher.Band.monoG.

Preamble

-- Generated from ChapterHermiteBandCalculusHigher.lean — theorem BookProof.HermiteBandHigher.Band.monoG
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterHermiteProductBasis
import Definitions.Def_ChapterYangMillsHermite
import Definitions.Def_ChapterNavierStokesDifferentialL2
import Mathlib
import Definitions.Def_ChapterHermiteBandCalculusHigher
import Definitions.Def_ChapterHermiteBandCalculus
open BookProof.HermiteBand
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.Band.monoG {T : MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ} {r M : ℕ}
    {C : ℝ} {g g' : ℕ → ℝ} (hC : 0 ≤ C) (hg : ∀ n, g n ≤ g' n) (h : Band T r M C g) :
    Band T r M C g' := by sorry

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