`BookProof.SmBrstGhost.sumStruct_antisymm` {ι κ : Type*} {f1 : ι → ι → ι → ℝ} {f2 : κ → κ → κ → ℝ} (h1 : ∀ a b c, f1 a b c = -f1 b a c) (h2 : ∀ a b c, f2 a b c = -f2 b...

Proved

BookProof.SmBrstGhost.sumStruct_antisymm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmBrstGhost.

BookProof.SmBrstGhost.sumStruct_antisymm {ι κ : Type*} {f1 : ι → ι → ι → ℝ} {f2 : κ → κ → κ → ℝ} (h1 : ∀ a b c, f1 a b c = -f1 b a c) (h2 : ∀ a b c, f2 a b c = -f2 b a c) (a b c : ι ⊕ κ) : sumStruct f1 f2 a b c = -sumStruct f1 f2 b a c

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

Preamble

-- Generated from ChapterSmBrstGhost.lean — theorem BookProof.SmBrstGhost.sumStruct_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.sumStruct_antisymm {ι κ : Type*} {f1 : ι → ι → ι → ℝ}
    {f2 : κ → κ → κ → ℝ} (h1 : ∀ a b c, f1 a b c = -f1 b a c)
    (h2 : ∀ a b c, f2 a b c = -f2 b a c) (a b c : ι ⊕ κ) :
    sumStruct f1 f2 a b c = -sumStruct f1 f2 b a c := by sorry

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