`BookProof.SmBrstGhost.ghostNumber_occ` (m : ℕ) (S : Finset (Fin (m + 12))) : ghostNumber m (occ S) = (Finset.univ.filter (fun a : Fin 12 => ghostMode m a ∈ S)).card • occ S

Proved

BookProof.SmBrstGhost.ghostNumber_occ

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmBrstGhost.

BookProof.SmBrstGhost.ghostNumber_occ (m : ℕ) (S : Finset (Fin (m + 12))) : ghostNumber m (occ S) = (Finset.univ.filter (fun a : Fin 12 => ghostMode m a ∈ S)).card • occ S

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

Preamble

-- Generated from ChapterSmBrstGhost.lean — theorem BookProof.SmBrstGhost.ghostNumber_occ
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterYangMillsSU3
import Mathlib
import Definitions.Def_ChapterSmBrstGhost
import Definitions.Def_ChapterNavierStokes
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.NavierStokes
open BookProof.SmCar
open BookProof.SmBrstGhost



open BookProof.SmCar BookProof.BRSTNilpotent BookProof.YangMillsSU3

noncomputable section

variable {m : ℕ}

Formal statement

theorem BookProof.SmBrstGhost.ghostNumber_occ (m : ℕ) (S : Finset (Fin (m + 12))) :
    ghostNumber m (occ S)
      = (Finset.univ.filter (fun a : Fin 12 => ghostMode m a ∈ S)).card • occ S := by sorry

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