`BookProof.SmGaugeRep.smGen_closes` (hS3 : ClosesWithStructureConstants S3 f3) (y : ℝ) : ClosesWithStructureConstants (smGen S3 y) (smStruct f3)

Proved

BookProof.SmGaugeRep.smGen_closes

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmGaugeRepresentation.

BookProof.SmGaugeRep.smGen_closes (hS3 : ClosesWithStructureConstants S3 f3) (y : ℝ) : ClosesWithStructureConstants (smGen S3 y) (smStruct f3)

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

Preamble

-- Generated from ChapterSmGaugeRepresentation.lean — theorem BookProof.SmGaugeRep.smGen_closes
import Mathlib
import Definitions.Def_ChapterSmGaugeRepresentation
import Definitions.Def_ChapterSmBrstGhost
import Definitions.Def_ChapterYangMillsSU3
open BookProof.SmBrstGhost
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.smGen_closes (hS3 : ClosesWithStructureConstants S3 f3) (y : ℝ) :
    ClosesWithStructureConstants (smGen S3 y) (smStruct f3) := by sorry

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