`BookProof.HermiteBandHigher.IsBandR.comp` {r₁ r₂ m₁ m₂ : ℕ} {T U : MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ} (hU : IsBandR r₂ m₂ U) (hT : IsBandR r₁ m₁ T)...

Proved

BookProof.HermiteBandHigher.IsBandR.comp

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteBandCalculusHigher.

BookProof.HermiteBandHigher.IsBandR.comp {r₁ r₂ m₁ m₂ : ℕ} {T U : MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ} (hU : IsBandR r₂ m₂ U) (hT : IsBandR r₁ m₁ T) : IsBandR (r₁ + r₂) (m₁ + m₂) (U ∘ₗ T)

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

Preamble

-- Generated from ChapterHermiteBandCalculusHigher.lean — theorem BookProof.HermiteBandHigher.IsBandR.comp
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.IsBandR.comp {r₁ r₂ m₁ m₂ : ℕ}
    {T U : MvPolynomial (Fin d) ℂ →ₗ[ℂ] MvPolynomial (Fin d) ℂ}
    (hU : IsBandR r₂ m₂ U) (hT : IsBandR r₁ m₁ T) :
    IsBandR (r₁ + r₂) (m₁ + m₂) (U ∘ₗ T) := by sorry

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