`BookProof.CoreBounds.coreExt_commForm_le_inc` [DecidableEq ι] {c : ι → ℝ} {H₀ : lpFiniteModes ι →ₗ[ℂ] L2I ι} {A B : ℝ} (hA : CoreRelBound c H₀ A) (hcomm : ∀ u :...

Proved

BookProof.CoreBounds.coreExt_commForm_le_inc

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoreBoundsEsa.

BookProof.CoreBounds.coreExt_commForm_le_inc [DecidableEq ι] {c : ι → ℝ} {H₀ : lpFiniteModes ι →ₗ[ℂ] L2I ι} {A B : ℝ} (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) (x : maxDom c) : |commForm (coreExt hA) (diagMax c) x| ≤ B * quadForm (diagMax c) x

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

Replaces the unuploadable node BookProof_CoreBounds_coreExt_commForm_le, 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.coreExt_commForm_le_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.coreExt_commForm_le_inc [DecidableEq ι] {c : ι → ℝ} {H₀ : lpFiniteModes ι →ₗ[ℂ] L2I ι}
    {A B : ℝ} (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)
    (x : maxDom c) :
    |commForm (coreExt hA) (diagMax c) x| ≤ B * quadForm (diagMax c) x := by sorry

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