Prove2Me

`BookProof.SmBrstGhost.fermiBilin_sum` {ι : Type*} (s : Finset ι) (M : ι → Matrix (Fin N) (Fin N) ℂ) : (fermiBilin (∑ t ∈ s, M t) : Module.End ℂ (FermiFock N)) = ∑ t ∈ s, fermiBili

Proved
BookProof.SmBrstGhost.fermiBilin_sum

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmBrstGhost.

BookProof.SmBrstGhost.fermiBilin_sum {ι : Type*} (s : Finset ι) (M : ι → Matrix (Fin N) (Fin N) ℂ) : (fermiBilin (∑ t ∈ s, M t) : Module.End ℂ (FermiFock N)) = ∑ t ∈ s, fermiBilin (M t)

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

Preamble
-- Generated from ChapterSmBrstGhost.lean — theorem BookProof.SmBrstGhost.fermiBilin_sum
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_sum {ι : Type*} (s : Finset ι) (M : ι → Matrix (Fin N) (Fin N) ℂ) :
    (fermiBilin (∑ t ∈ s, M t) : Module.End ℂ (FermiFock N))
      = ∑ t ∈ s, fermiBilin (M t) := by sorry

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