`BookProof.NavierStokesFlow.FockOfFock.intervalDens_mul_extField_eq` (j : ℕ) : (fun ξ => extField ξ * intervalDens j ξ) = Set.indicator (Set.Ioc (j : ℝ) ((j : ℝ) + 1)) (fun ξ => ξ

Proved

BookProof.NavierStokesFlow.FockOfFock.intervalDens_mul_extField_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFockEsa.

BookProof.NavierStokesFlow.FockOfFock.intervalDens_mul_extField_eq (j : ℕ) : (fun ξ => extField ξ * intervalDens j ξ) = Set.indicator (Set.Ioc (j : ℝ) ((j : ℝ) + 1)) (fun ξ => ξ ^ 2)

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.FockOfFock.intervalDens_mul_extField_eq.

Preamble

-- Generated from ChapterNavierStokesFockEsa.lean — theorem BookProof.NavierStokesFlow.FockOfFock.intervalDens_mul_extField_eq
import Mathlib
import Definitions.Def_ChapterNavierStokesFockEsa
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesFockSpace
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.FockOfFock


open MeasureTheory



open FullEsa LagrangianEsa

variable {M : Type*} [DecidableEq M]
variable {M : Type*} [DecidableEq M] {Ω : Type*} [MeasurableSpace Ω]
variable {J K : Type*} [DecidableEq J] [DecidableEq K]
variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
variable {K : Type*} [DecidableEq K]

Formal statement

theorem BookProof.NavierStokesFlow.FockOfFock.intervalDens_mul_extField_eq (j : ℕ) :
    (fun ξ => extField ξ * intervalDens j ξ)
      = Set.indicator (Set.Ioc (j : ℝ) ((j : ℝ) + 1)) (fun ξ => ξ ^ 2) := by sorry

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