Prove2Me

(L : List (SignedHop ι sym)) : ∃ a b : ℝ, 0 ≤ a ∧ 0 ≤ b ∧ ∀ x : maxDom sym, ‖(listH L x : L2I ι)‖ ^ 2 ≤ a * ‖(diagMax sym x : L2I ι)‖ ^ 2 + b * ‖(x : L2I ι)‖ ^ 2

Proved
BookProof.NavierStokesFlow.SignedShift.listH_relative_bound

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

navier-stokesoperator-algebrastimepiece

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

Preamble
-- Generated from ChapterNavierStokesSignedShift.lean — theorem BookProof.NavierStokesFlow.SignedShift.listH_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.HermiteFarisLavine









open scoped ENNReal




variable {ι : Type*}



variable {sym : ι → ℝ} (S : SignedHop ι sym)


































variable {sym : ι → ℝ}
Formal statement
theorem BookProof.NavierStokesFlow.SignedShift.listH_relative_bound (L : List (SignedHop ι sym)) :
    ∃ a b : ℝ, 0 ≤ a ∧ 0 ≤ b ∧ ∀ x : maxDom sym,
      ‖(listH L x : L2I ι)‖ ^ 2
        ≤ a * ‖(diagMax sym x : L2I ι)‖ ^ 2 + b * ‖(x : L2I ι)‖ ^ 2 := by sorry
Source
https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterNavierStokesFlow.lean

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