`BookProof.HermiteBandHigher.isBand1_iff_isBandDeg_one` {T : MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ} : IsBand1 T → IsBandDeg 1 T

Proved

BookProof.HermiteBandHigher.isBand1_iff_isBandDeg_one

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteBandCalculusHigher.

BookProof.HermiteBandHigher.isBand1_iff_isBandDeg_one {T : MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ} : IsBand1 T → IsBandDeg 1 T

Formalization note: Lean 4 identifier BookProof.HermiteBandHigher.isBand1_iff_isBandDeg_one.

Preamble

-- Generated from ChapterHermiteBandCalculusHigher.lean — theorem BookProof.HermiteBandHigher.isBand1_iff_isBandDeg_one
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.isBand1_iff_isBandDeg_one {T : MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ} :
    IsBand1 T → IsBandDeg 1 T := by sorry

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