`BookProof.QgPhysicalSectorIdentity.int_L_gf_eq_zero_physical` (I : BrstIntegral S.toGaugeFixingSystem) : I.int (sTop S.toGaugeFixingSystem (Psi S.toGaugeFixingSystem)) = 0

Proved

BookProof.QgPhysicalSectorIdentity.int_L_gf_eq_zero_physical

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQgPhysicalSectorIdentity.

BookProof.QgPhysicalSectorIdentity.int_L_gf_eq_zero_physical (I : BrstIntegral S.toGaugeFixingSystem) : I.int (sTop S.toGaugeFixingSystem (Psi S.toGaugeFixingSystem)) = 0

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

Preamble

-- Generated from ChapterQgPhysicalSectorIdentity.lean — theorem BookProof.QgPhysicalSectorIdentity.int_L_gf_eq_zero_physical
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
import Definitions.Def_ChapterGaugeFixing
open BookProof.GaugeFixing
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)

Formal statement

theorem BookProof.QgPhysicalSectorIdentity.int_L_gf_eq_zero_physical (I : BrstIntegral S.toGaugeFixingSystem) :
    I.int (sTop S.toGaugeFixingSystem (Psi S.toGaugeFixingSystem)) = 0 := by sorry

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