`BookProof.NsBrstDerivativeGauge.nsHamiltonian2_mapsTo_ker` (nu : ℂ) {v : NSGraded} (hv : nsDerivBrstCharge2 v = 0) : nsDerivBrstCharge2 (nsHamiltonian2 nu v) = 0

Proved

BookProof.NsBrstDerivativeGauge.nsHamiltonian2_mapsTo_ker

by leonardopedro · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsBrstDerivativeGauge.

BookProof.NsBrstDerivativeGauge.nsHamiltonian2_mapsTo_ker (nu : ℂ) {v : NSGraded} (hv : nsDerivBrstCharge2 v = 0) : nsDerivBrstCharge2 (nsHamiltonian2 nu v) = 0

Formalization note: Lean 4 identifier BookProof.NsBrstDerivativeGauge.nsHamiltonian2_mapsTo_ker.

Preamble

-- Generated from ChapterNsBrstDerivativeGauge.lean — theorem BookProof.NsBrstDerivativeGauge.nsHamiltonian2_mapsTo_ker
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterQuantumGravityBrstCharge
import Definitions.Def_ChapterNavierStokesGaugeY2
import Mathlib
import Definitions.Def_ChapterNsBrstDerivativeGauge
import Definitions.Def_ChapterNavierStokesGaugeY
open BookProof.NavierStokesGaugeY
open BookProof.NsBrstDerivativeGauge



open MvPolynomial BookProof.BRSTNilpotent BookProof.QuantumGravityBrstCharge
open BookProof.NavierStokesGaugeY BookProof.NavierStokesGaugeY2

noncomputable section

Formal statement

theorem BookProof.NsBrstDerivativeGauge.nsHamiltonian2_mapsTo_ker (nu : ℂ) {v : NSGraded} (hv : nsDerivBrstCharge2 v = 0) :
    nsDerivBrstCharge2 (nsHamiltonian2 nu v) = 0 := by sorry

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