`BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_relative_bound` (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) : ‖(nsH κ hκ x : L2I ℕ)‖ ^ 2 ≤ (1 / 2) * ‖(diagMax (oscSymbol κ) x : L2I

Proved

BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_relative_bound

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesHermiteFarisLavine.

BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_relative_bound (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) : ‖(nsH κ hκ x : L2I ℕ)‖ ^ 2 ≤ (1 / 2) * ‖(diagMax (oscSymbol κ) x : L2I ℕ)‖ ^ 2 + (2 * κ ^ 2) * ‖(x : L2I ℕ)‖ ^ 2

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

Preamble

-- Generated from ChapterNavierStokesHermiteFarisLavine.lean — theorem BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_relative_bound
import Mathlib
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesSignedShift
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.SignedShift
open BookProof.NavierStokesFlow.SignedShift.SignedHop
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_relative_bound (hκ : 0 ≤ κ) (x : maxDom (oscSymbol κ)) :
    ‖(nsH κ hκ x : L2I ℕ)‖ ^ 2
      ≤ (1 / 2) * ‖(diagMax (oscSymbol κ) x : L2I ℕ)‖ ^ 2 + (2 * κ ^ 2) * ‖(x : L2I ℕ)‖ ^ 2 := by sorry

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