`BookProof.NavierStokesFlow.AffineFiber.PairShift.pairH_commForm_bound` (x : maxDom P.sym) : |commForm (pairH P) (diagMax P.sym) x| ≤ (2 * P.step₁ * (1 / 4 + P.K) + 2 * P.step₂ * (

Proved

BookProof.NavierStokesFlow.AffineFiber.PairShift.pairH_commForm_bound

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesAffineFiberEsa.

BookProof.NavierStokesFlow.AffineFiber.PairShift.pairH_commForm_bound (x : maxDom P.sym) : |commForm (pairH P) (diagMax P.sym) x| ≤ (2 * P.step₁ * (1 / 4 + P.K) + 2 * P.step₂ * (1 / 4 + P.K)) * quadForm (diagMax P.sym) x

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.AffineFiber.PairShift.pairH_commForm_bound.

Preamble

-- Generated from ChapterNavierStokesAffineFiberEsa.lean — theorem BookProof.NavierStokesFlow.AffineFiber.PairShift.pairH_commForm_bound
import Mathlib
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesShiftHamiltonian
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.ShiftHamiltonian.ShiftData
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.AffineFiber


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato HermiteFarisLavine ShiftHamiltonian

variable {ι : Type*}

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {D : Submodule ℂ F}
variable (P : PairShift ι)

Formal statement

theorem BookProof.NavierStokesFlow.AffineFiber.PairShift.pairH_commForm_bound (x : maxDom P.sym) :
    |commForm (pairH P) (diagMax P.sym) x|
      ≤ (2 * P.step₁ * (1 / 4 + P.K) + 2 * P.step₂ * (1 / 4 + P.K))
        * quadForm (diagMax P.sym) x := by sorry

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