Prove2Me

(x : maxDom sym) : ‖(hopH S x : L2I ι)‖ ^ 2 ≤ (1 / 2) * ‖(diagMax sym x : L2I ι)‖ ^ 2 + (8 * S.K ^ 2) * ‖(x : L2I ι)‖ ^ 2

Proved
BookProof.NavierStokesFlow.SignedShift.SignedHop.hopH_relative_bound

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

navier-stokesoperator-algebrastimepiece

Lean 4 theorem BookProof.NavierStokesFlow.SignedShift.SignedHop.hopH_relative_bound (module BookProof.NavierStokesFlow), source chapter BookProof/ChapterNavierStokesFlow.lean.

Preamble
-- Generated from ChapterNavierStokesSignedShift.lean — theorem BookProof.NavierStokesFlow.SignedShift.SignedHop.hopH_relative_bound
import Mathlib
import Definitions.Def_ChapterNavierStokesSignedShift
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.SignedShift
open BookProof.NavierStokesFlow.LpNat BookProof.FarisLavine BookProof.NavierStokesFlow.IkebeKato BookProof.NavierStokesFlow.ShiftHamiltonian BookProof.NavierStokesFlow.AffineFiber
open BookProof.NavierStokesFlow.SignedShift.SignedHop









open scoped ENNReal




variable {ι : Type*}



variable {sym : ι → ℝ} (S : SignedHop ι sym)
Formal statement
theorem BookProof.NavierStokesFlow.SignedShift.SignedHop.hopH_relative_bound (x : maxDom sym) :
    ‖(hopH S x : L2I ι)‖ ^ 2
      ≤ (1 / 2) * ‖(diagMax sym x : L2I ι)‖ ^ 2 + (8 * S.K ^ 2) * ‖(x : L2I ι)‖ ^ 2 := by sorry
Source
https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterNavierStokesFlow.lean

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