`BookProof.SmCar.fermiBilin_symmetric` {h : Matrix (Fin n) (Fin n) ℂ} (hh : h.conjTranspose = h) (ψ φ : FermiFock n) : (inner ℂ (fermiBilin h ψ) φ : ℂ) = inner ℂ ψ (fermiBilin h φ)

Proved

BookProof.SmCar.fermiBilin_symmetric

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmCarAlgebra.

BookProof.SmCar.fermiBilin_symmetric {h : Matrix (Fin n) (Fin n) ℂ} (hh : h.conjTranspose = h) (ψ φ : FermiFock n) : (inner ℂ (fermiBilin h ψ) φ : ℂ) = inner ℂ ψ (fermiBilin h φ)

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

Preamble

-- Generated from ChapterSmCarAlgebra.lean — theorem BookProof.SmCar.fermiBilin_symmetric
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_symmetric {h : Matrix (Fin n) (Fin n) ℂ} (hh : h.conjTranspose = h)
    (ψ φ : FermiFock n) :
    (inner ℂ (fermiBilin h ψ) φ : ℂ) = inner ℂ ψ (fermiBilin h φ) := by sorry

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