`BookProof.SmBrstGhost.fermiBilin_sub` (M P : Matrix (Fin N) (Fin N) ℂ) : (fermiBilin (M - P) : Module.End ℂ (FermiFock N)) = fermiBilin M - fermiBilin P

Proved

BookProof.SmBrstGhost.fermiBilin_sub

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmBrstGhost.

BookProof.SmBrstGhost.fermiBilin_sub (M P : Matrix (Fin N) (Fin N) ℂ) : (fermiBilin (M - P) : Module.End ℂ (FermiFock N)) = fermiBilin M - fermiBilin P

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

Preamble

-- Generated from ChapterSmBrstGhost.lean — theorem BookProof.SmBrstGhost.fermiBilin_sub
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterYangMillsSU3
import Mathlib
import Definitions.Def_ChapterSmBrstGhost
import Definitions.Def_ChapterNavierStokesFockSpace
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.NavierStokesFlow.FockOfFock
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_sub (M P : Matrix (Fin N) (Fin N) ℂ) :
    (fermiBilin (M - P) : Module.End ℂ (FermiFock N)) = fermiBilin M - fermiBilin P := by sorry

View graph