(hκ : ∀ i, 0 ≤ κ i) : (lpFiniteModes (Occ d)).subtype.comp ((∑ i, ((mom κ i).comp (mom κ i) + (drift κ i).comp (drift κ i))) + LinearMap.id) = (diagMax (fockSym κ)).comp...

-- Generated from ChapterNavierStokesFockCanonical.lean — theorem BookProof.NavierStokesFlow.FockCanonical.fock_comparison_eq
import Mathlib
import Definitions.Def_ChapterNavierStokesFockCanonical
import Definitions.Def_ChapterBosonicCCR
import Definitions.Def_ChapterNavierStokesCanonicalVector
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesFlow
import Definitions.Def_ChapterNavierStokesFockManyMode
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.Bosonic
open BookProof.NavierStokesFlow.CanonicalVector
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.FockCanonical

variable {d : ℕ} {κ : Fin d → ℝ}


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato ShiftHamiltonian FockManyMode HermiteCanonical

theorem BookProof.NavierStokesFlow.FockCanonical.fock_comparison_eq (hκ : ∀ i, 0 ≤ κ i) :
    (lpFiniteModes (Occ d)).subtype.comp
        ((∑ i, ((mom κ i).comp (mom κ i) + (drift κ i).comp (drift κ i))) + LinearMap.id)
      = (diagMax (fockSym κ)).comp
        (Submodule.inclusion (finiteModes_le_maxDom (fockSym κ))) := by sorry