`BookProof.SmBrstGhost.fermiBilin_comm_creat` {A : Matrix (Fin N) (Fin N) ℂ} {k : Fin N} (hcol : ∀ i, A i k = 0) : (fermiBilin A : Module.End ℂ (FermiFock N)) * creat k = creat k *

Proved

BookProof.SmBrstGhost.fermiBilin_comm_creat

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmBrstGhost.

BookProof.SmBrstGhost.fermiBilin_comm_creat {A : Matrix (Fin N) (Fin N) ℂ} {k : Fin N} (hcol : ∀ i, A i k = 0) : (fermiBilin A : Module.End ℂ (FermiFock N)) * creat k = creat k * fermiBilin A

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

Preamble

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



open BookProof.SmCar BookProof.BRSTNilpotent BookProof.YangMillsSU3

noncomputable section

variable {m : ℕ}
variable {R : Type*} [Ring R] [Algebra ℝ R] {n : ℕ}
variable {N : ℕ}

Formal statement

theorem BookProof.SmBrstGhost.fermiBilin_comm_creat {A : Matrix (Fin N) (Fin N) ℂ} {k : Fin N}
    (hcol : ∀ i, A i k = 0) :
    (fermiBilin A : Module.End ℂ (FermiFock N)) * creat k
      = creat k * fermiBilin A := by sorry

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