`BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_commForm_bound` (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) : |commForm (nsH κ hκ) (diagMax (oscSymbol κ)) x| ≤ (2 * κ + 4 * κ ^ 2) *

Proved

BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_commForm_bound

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesHermiteFarisLavine.

BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_commForm_bound (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) : |commForm (nsH κ hκ) (diagMax (oscSymbol κ)) x| ≤ (2 * κ + 4 * κ ^ 2) * quadForm (diagMax (oscSymbol κ)) x

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_commForm_bound.

Preamble

-- Generated from ChapterNavierStokesHermiteFarisLavine.lean — theorem BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_commForm_bound
import Mathlib
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.HermiteFarisLavine


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato

variable {κ : ℝ}
variable {x : maxDom (oscSymbol κ)}

Formal statement

theorem BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_commForm_bound (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) :
    |commForm (nsH κ hκ) (diagMax (oscSymbol κ)) x|
      ≤ (2 * κ + 4 * κ ^ 2) * quadForm (diagMax (oscSymbol κ)) x := by sorry

View graph