`BookProof.NavierStokesFlow.FockLagrangian.vacState_coeFn` : ((vacState : Lp ℂ 2 fockR) : ParcelConf ℝ → ℂ) =ᵐ[fockR] vacSet.indicator (fun _ => (1 : ℂ))

Proved

BookProof.NavierStokesFlow.FockLagrangian.vacState_coeFn

by leonardopedro · Oct 18, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFockParcels.

BookProof.NavierStokesFlow.FockLagrangian.vacState_coeFn : ((vacState : Lp ℂ 2 fockR) : ParcelConf ℝ → ℂ) =ᵐ[fockR] vacSet.indicator (fun _ => (1 : ℂ))

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

Preamble

-- Generated from ChapterNavierStokesFockParcels.lean — theorem BookProof.NavierStokesFlow.FockLagrangian.vacState_coeFn
import Mathlib
import Definitions.Def_ChapterNavierStokesFockParcels
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesFockLagrangian
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.FockLagrangian


open MeasureTheory



open FullEsa FockContinuum

variable {Ω : Type*} [MeasurableSpace Ω]

Formal statement

theorem BookProof.NavierStokesFlow.FockLagrangian.vacState_coeFn :
    ((vacState : Lp ℂ 2 fockR) : ParcelConf ℝ → ℂ)
      =ᵐ[fockR] vacSet.indicator (fun _ => (1 : ℂ)) := by sorry

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