`BookProof.SmCar.fermiBilin_apply` (h : Matrix (Fin n) (Fin n) ℂ) (ψ : FermiFock n) : fermiBilin h ψ = ∑ i : Fin n, ∑ j : Fin n, h i j • creat i (annih j ψ)

Proved

BookProof.SmCar.fermiBilin_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmCarAlgebra.

BookProof.SmCar.fermiBilin_apply (h : Matrix (Fin n) (Fin n) ℂ) (ψ : FermiFock n) : fermiBilin h ψ = ∑ i : Fin n, ∑ j : Fin n, h i j • creat i (annih j ψ)

Formalization note: Lean 4 identifier BookProof.SmCar.fermiBilin_apply.

Preamble

-- Generated from ChapterSmCarAlgebra.lean — theorem BookProof.SmCar.fermiBilin_apply
import Mathlib
import Definitions.Def_ChapterSmCarAlgebra
import Definitions.Def_ChapterNavierStokesFockSpace
open BookProof.NavierStokesFlow.FockOfFock
open BookProof.SmCar



open Finset

variable {n : ℕ}

Formal statement

theorem BookProof.SmCar.fermiBilin_apply (h : Matrix (Fin n) (Fin n) ℂ) (ψ : FermiFock n) :
    fermiBilin h ψ = ∑ i : Fin n, ∑ j : Fin n, h i j • creat i (annih j ψ) := by sorry

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