Prove2Me

`BookProof.QgPhysicalSectorIdentity.lagrange_term_zero_of_fixing` (hfix : gaugeField S.toGaugeFixingSystem = S.toGaugeFixingSystem.zero (1, 0)) : S.mul (1, 0) (1, 0) S.B (gaugeFiel

Proved
BookProof.QgPhysicalSectorIdentity.lagrange_term_zero_of_fixing

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQgPhysicalSectorIdentity.

BookProof.QgPhysicalSectorIdentity.lagrange_term_zero_of_fixing (hfix : gaugeField S.toGaugeFixingSystem = S.toGaugeFixingSystem.zero (1, 0)) : S.mul (1, 0) (1, 0) S.B (gaugeField S.toGaugeFixingSystem) = S.zero (2, 0)

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

Preamble
-- Generated from ChapterQgPhysicalSectorIdentity.lean — theorem BookProof.QgPhysicalSectorIdentity.lagrange_term_zero_of_fixing
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
import Definitions.Def_ChapterSirkFinitePrecision
open BookProof.GaugeFixing
open BookProof.SirkFinitePrecision
open BookProof.SirkFinitePrecision.CertInterval
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.lagrange_term_zero_of_fixing
    (hfix : gaugeField S.toGaugeFixingSystem = S.toGaugeFixingSystem.zero (1, 0)) :
    S.mul (1, 0) (1, 0) S.B (gaugeField S.toGaugeFixingSystem) = S.zero (2, 0) := by sorry

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