Prove2Me

`BookProof.SmGaugeRep.sm_brst_nilpotent_rep` (hS3 : TraceOrthonormal S3) (hf3 : ClosesWithStructureConstants S3 f3) (y : ℝ) : smBrstCharge 6 (smGen S3 y) f3 * smBrstCharge 6 (smGen

Proved
BookProof.SmGaugeRep.sm_brst_nilpotent_rep

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmGaugeRepresentation.

BookProof.SmGaugeRep.sm_brst_nilpotent_rep (hS3 : TraceOrthonormal S3) (hf3 : ClosesWithStructureConstants S3 f3) (y : ℝ) : smBrstCharge 6 (smGen S3 y) f3 * smBrstCharge 6 (smGen S3 y) f3 = 0

Formalization note: Lean 4 identifier BookProof.SmGaugeRep.sm_brst_nilpotent_rep.

Preamble
-- Generated from ChapterSmGaugeRepresentation.lean — theorem BookProof.SmGaugeRep.sm_brst_nilpotent_rep
import Mathlib
import Definitions.Def_ChapterSmGaugeRepresentation
import Definitions.Def_ChapterSmBrstGhost
import Definitions.Def_ChapterSmCarAlgebra
import Definitions.Def_ChapterYangMillsSU3
open BookProof.SmBrstGhost
open BookProof.SmCar
open BookProof.YangMillsSU3
open BookProof.SmGaugeRep



open Matrix Kronecker
open BookProof.YangMillsSU3 BookProof.SmBrstGhost

noncomputable section

variable {S3 : Fin 8 → Matrix (Fin 3) (Fin 3) ℂ} {f3 : Fin 8 → Fin 8 → Fin 8 → ℝ}
Formal statement
theorem BookProof.SmGaugeRep.sm_brst_nilpotent_rep (hS3 : TraceOrthonormal S3)
    (hf3 : ClosesWithStructureConstants S3 f3) (y : ℝ) :
    smBrstCharge 6 (smGen S3 y) f3 * smBrstCharge 6 (smGen S3 y) f3 = 0 := by sorry

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