(i : Fin d) : (cre i - ann i).comp (cre i + ann i) + (cre i + ann i).comp (cre i - ann i) = (2 : ℂ) • ((cre i).comp (cre i) - (ann i).comp (ann i))

-- Generated from ChapterNavierStokesFockCanonical.lean — theorem BookProof.NavierStokesFlow.FockCanonical.anti_DS
import Mathlib
import Definitions.Def_ChapterNavierStokesFockCanonical
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.FockCanonical







open scoped ENNReal



open BookProof.NavierStokesFlow.LpNat BookProof.FarisLavine BookProof.NavierStokesFlow.IkebeKato BookProof.NavierStokesFlow.ShiftHamiltonian BookProof.NavierStokesFlow.FockManyMode BookProof.NavierStokesFlow.HermiteCanonical

variable {d : ℕ} {κ : Fin d → ℝ}

theorem BookProof.NavierStokesFlow.FockCanonical.anti_DS (i : Fin d) :
    (cre i - ann i).comp (cre i + ann i) + (cre i + ann i).comp (cre i - ann i)
      = (2 : ℂ) • ((cre i).comp (cre i) - (ann i).comp (ann i)) := by sorry