`BookProof.NavierStokesFlow.FockLagrangian.bigState_symbol_ge` {K : ℝ} (hK : 1 ≤ K) : ∀ᵐ x ∂fockR, ((bigState K : Lp ℂ 2 fockR) : ParcelConf ℝ → ℂ) x ≠ 0 → K ≤...

Proved

BookProof.NavierStokesFlow.FockLagrangian.bigState_symbol_ge

by leonardopedro · Oct 22, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFockParcels.

BookProof.NavierStokesFlow.FockLagrangian.bigState_symbol_ge {K : ℝ} (hK : 1 ≤ K) : ∀ᵐ x ∂fockR, ((bigState K : Lp ℂ 2 fockR) : ParcelConf ℝ → ℂ) x ≠ 0 → K ≤ |momFock.total x| := by filter_upwards [bigState_coeFn K] with x hx hne rw [hx] at hne have hmem : x ∈ bigSet K

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.FockLagrangian.bigState_symbol_ge.

Preamble

-- Generated from ChapterNavierStokesFockParcels.lean — theorem BookProof.NavierStokesFlow.FockLagrangian.bigState_symbol_ge
import Mathlib
import Definitions.Def_ChapterNavierStokesFockParcels
import Definitions.Def_ChapterNavierStokesThreeComponent
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesFockLagrangian
import Definitions.Def_ChapterShiftedQuadraticEsa
open BookProof.NavierStokesFlow.ThreeComponent
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.FockLagrangian


open MeasureTheory



open FullEsa FockContinuum

variable {Ω : Type*} [MeasurableSpace Ω]

Formal statement

theorem BookProof.NavierStokesFlow.FockLagrangian.bigState_symbol_ge {K : ℝ} (hK : 1 ≤ K) :
    ∀ᵐ x ∂fockR, ((bigState K : Lp ℂ 2 fockR) : ParcelConf ℝ → ℂ) x ≠ 0
        → K ≤ |momFock.total x| := by sorry

View graph