`BookProof.CoreBounds.norm_coreExt_le_inc` [DecidableEq ι] {c : ι → ℝ} {H₀ : lpFiniteModes ι →ₗ[ℂ] L2I ι} {A : ℝ} (hA : CoreRelBound c H₀ A) (x : maxDom c) : ‖coreExt hA...

Proved

BookProof.CoreBounds.norm_coreExt_le_inc

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoreBoundsEsa.

BookProof.CoreBounds.norm_coreExt_le_inc [DecidableEq ι] {c : ι → ℝ} {H₀ : lpFiniteModes ι →ₗ[ℂ] L2I ι} {A : ℝ} (hA : CoreRelBound c H₀ A) (x : maxDom c) : ‖coreExt hA x‖ ≤ A * ‖(diagMax c x : L2I ι)‖

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

Replaces the unuploadable node BookProof_CoreBounds_norm_coreExt_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.norm_coreExt_le_inc
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterOperatorSeriesEsa
import Mathlib
import Definitions.Def_ChapterCoreBoundsEsa
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.norm_coreExt_le_inc [DecidableEq ι] {c : ι → ℝ} {H₀ : lpFiniteModes ι →ₗ[ℂ] L2I ι} {A : ℝ}
    (hA : CoreRelBound c H₀ A) (x : maxDom c) :
    ‖coreExt hA x‖ ≤ A * ‖(diagMax c x : L2I ι)‖ := by sorry

View graph