`BookProof.CoreBounds.essentiallySelfAdjointOn_finiteModes_of_core_bounds_inc` (c : ι → ℝ) (hc : ∀ k, 0 ≤ c k) (H₀ : lpFiniteModes ι →ₗ[ℂ] L2I ι) (A B : ℝ) (hB : 0 ≤ B)...

Proved

BookProof.CoreBounds.essentiallySelfAdjointOn_finiteModes_of_core_bounds_inc

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoreBoundsEsa.

BookProof.CoreBounds.essentiallySelfAdjointOn_finiteModes_of_core_bounds_inc (c : ι → ℝ) (hc : ∀ k, 0 ≤ c k) (H₀ : lpFiniteModes ι →ₗ[ℂ] L2I ι) (A B : ℝ) (hB : 0 ≤ B) (hsym : ∀ u v : lpFiniteModes ι, (inner ℂ (H₀ u) ((v : L2I ι)) : ℂ) = inner ℂ ((u : L2I ι)) (H₀ v)) (hA : CoreRelBound c H₀ A) (hcomm : ∀ u : lpFiniteModes ι, |(-2 : ℝ) * (inner ℂ (H₀ u) ((diagMax c (inclC c u) : L2I ι)) : ℂ).im| ≤ B * (inner ℂ ((u : L2I ι)) ((diagMax c (inclC c u) : L2I ι)) : ℂ).re) : EssentiallySelfAdjointOn (lpFiniteModes ι) H₀

Formalization note: Lean 4 identifier BookProof.CoreBounds.essentiallySelfAdjointOn_finiteModes_of_core_bounds_inc.

Replaces the unuploadable node BookProof_CoreBounds_essentiallySelfAdjointOn_finiteModes_of_core_bounds, whose statement name is already declared inside its published definition bundle; the _inc suffix publishes the same statement as its own node.

Preamble

-- Generated from ChapterCoreBoundsEsa.lean — theorem BookProof.CoreBounds.essentiallySelfAdjointOn_finiteModes_of_core_bounds_inc
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterOperatorSeriesEsa
import Mathlib
import Definitions.Def_ChapterCoreBoundsEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
open BookProof.NavierStokesFlow.IkebeKato
open BookProof.CoreBounds



open BookProof.FarisLavine BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato
open BookProof.OperatorSeries
open Filter Topology

noncomputable section

variable {ι : Type*} {c : ι → ℝ}

variable (H₀ : lpFiniteModes ι →ₗ[ℂ] L2I ι) (A : ℝ)

Formal statement

theorem BookProof.CoreBounds.essentiallySelfAdjointOn_finiteModes_of_core_bounds_inc
    (c : ι → ℝ) (hc : ∀ k, 0 ≤ c k) (H₀ : lpFiniteModes ι →ₗ[ℂ] L2I ι) (A B : ℝ) (hB : 0 ≤ B)
    (hsym : ∀ u v : lpFiniteModes ι,
      (inner ℂ (H₀ u) ((v : L2I ι)) : ℂ) = inner ℂ ((u : L2I ι)) (H₀ v))
    (hA : CoreRelBound c H₀ A)
    (hcomm : ∀ u : lpFiniteModes ι,
      |(-2 : ℝ) * (inner ℂ (H₀ u) ((diagMax c (inclC c u) : L2I ι)) : ℂ).im|
        ≤ B * (inner ℂ ((u : L2I ι)) ((diagMax c (inclC c u) : L2I ι)) : ℂ).re) :
    EssentiallySelfAdjointOn (lpFiniteModes ι) H₀ := by sorry

View graph