`BookProof.SmBrstGhost.smStruct_antisymm` {f3 : Fin 8 → Fin 8 → Fin 8 → ℝ} (h3 : ∀ a b c, f3 a b c = -f3 b a c) (a b c : Fin 12) : smStruct f3 a b c = -smStruct f3 b a c

Proved

BookProof.SmBrstGhost.smStruct_antisymm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmBrstGhost.

BookProof.SmBrstGhost.smStruct_antisymm {f3 : Fin 8 → Fin 8 → Fin 8 → ℝ} (h3 : ∀ a b c, f3 a b c = -f3 b a c) (a b c : Fin 12) : smStruct f3 a b c = -smStruct f3 b a c

Formalization note: Lean 4 identifier BookProof.SmBrstGhost.smStruct_antisymm.

Preamble

-- Generated from ChapterSmBrstGhost.lean — theorem BookProof.SmBrstGhost.smStruct_antisymm
import Definitions.Def_ChapterSmCarAlgebra
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterYangMillsSU3
import Mathlib
import Definitions.Def_ChapterSmBrstGhost
open BookProof.SmBrstGhost



open BookProof.SmCar BookProof.BRSTNilpotent BookProof.YangMillsSU3

noncomputable section

Formal statement

theorem BookProof.SmBrstGhost.smStruct_antisymm {f3 : Fin 8 → Fin 8 → Fin 8 → ℝ}
    (h3 : ∀ a b c, f3 a b c = -f3 b a c) (a b c : Fin 12) :
    smStruct f3 a b c = -smStruct f3 b a c := by sorry

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