`BookProof.QgPhysicalSectorIdentity.coupling_weighted_summable` {ω : ι → ℝ} (h : ι × ι → ℂ) (hsum : Summable fun k : ι × ι => ‖h k‖ * (ω k.1 + ω k.2 + 2)) : Summable fun k...

Proved

BookProof.QgPhysicalSectorIdentity.coupling_weighted_summable

by leonardopedro · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQgPhysicalSectorIdentity.

BookProof.QgPhysicalSectorIdentity.coupling_weighted_summable {ω : ι → ℝ} (h : ι × ι → ℂ) (hsum : Summable fun k : ι × ι => ‖h k‖ * (ω k.1 + ω k.2 + 2)) : Summable fun k : ι × ι => ‖h k‖ * (wsum ω (creIdx k.1) + wsum ω (annIdx k.2) + 2)

Formalization note: Lean 4 identifier BookProof.QgPhysicalSectorIdentity.coupling_weighted_summable.

Preamble

-- Generated from ChapterQgPhysicalSectorIdentity.lean — theorem BookProof.QgPhysicalSectorIdentity.coupling_weighted_summable
import Definitions.Def_ChapterGaugeFixing
import Definitions.Def_ChapterFockQuadraticEsa
import Definitions.Def_ChapterOperatorSeriesEsa
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesDeficiency
import Definitions.Def_ChapterNavierStokesIkebeKato
import Mathlib
import Definitions.Def_ChapterQgPhysicalSectorIdentity
open BookProof.QgPhysicalSectorIdentity



open BookProof.GaugeFixing
open BookProof.FockQuadratic
open BookProof.OperatorSeries
open BookProof.FarisLavine
open BookProof.NavierStokesFlow BookProof.NavierStokesFlow.LpNat
open BookProof.NavierStokesFlow.IkebeKato
open scoped ENNReal

variable {F : BiDegree → Type} (S : DerivativeVariableFixingSystem F)
variable {ι : Type*}

Formal statement

theorem BookProof.QgPhysicalSectorIdentity.coupling_weighted_summable {ω : ι → ℝ} (h : ι × ι → ℂ)
    (hsum : Summable fun k : ι × ι => ‖h k‖ * (ω k.1 + ω k.2 + 2)) :
    Summable fun k : ι × ι => ‖h k‖ * (wsum ω (creIdx k.1) + wsum ω (annIdx k.2) + 2) := by sorry

View graph