`BookProof.HermiteBandHigher.isBandDeg_mulOp_multiset` (s : Multiset (Fin d)) : IsBandDeg (Multiset.card s) (mulOp ((s.map (fun i => (X i : MvPolynomial (Fin d) ℂ))).prod))

Proved

BookProof.HermiteBandHigher.isBandDeg_mulOp_multiset

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteBandCalculusHigher.

BookProof.HermiteBandHigher.isBandDeg_mulOp_multiset (s : Multiset (Fin d)) : IsBandDeg (Multiset.card s) (mulOp ((s.map (fun i => (X i : MvPolynomial (Fin d) ℂ))).prod))

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

Preamble

-- Generated from ChapterHermiteBandCalculusHigher.lean — theorem BookProof.HermiteBandHigher.isBandDeg_mulOp_multiset
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterHermiteProductBasis
import Definitions.Def_ChapterHermiteBandCalculus
import Definitions.Def_ChapterYangMillsHermite
import Mathlib
import Definitions.Def_ChapterHermiteBandCalculusHigher
import Definitions.Def_ChapterF7
import Definitions.Def_ChapterNavierStokesDifferentialL2
open BookProof.ChapterF7
open BookProof.NavierStokesFlow.DifferentialL2
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.isBandDeg_mulOp_multiset (s : Multiset (Fin d)) :
    IsBandDeg (Multiset.card s)
      (mulOp ((s.map (fun i => (X i : MvPolynomial (Fin d) ℂ))).prod)) := by sorry

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