(hκ : ∀ i, 0 ≤ κ i) (x : maxDom (fockSym κ)) : commForm (fockH hκ) (diagMax (fockSym κ)) x = ∑ i, commForm (ShiftData.shiftH (modeData hκ i)) (diagMax (fockSym κ)) x

Proved

BookProof.NavierStokesFlow.FockManyMode.commForm_fockH

by leonardopedro · Oct 2, 2026 · Mathlib 0df444a (Lean v4.33.1)

navier-stokesoperator-algebrastimepiece

Lean 4 theorem BookProof.NavierStokesFlow.FockManyMode.commForm_fockH (module BookProof.NavierStokesFlow), source chapter BookProof/ChapterNavierStokesFlow.lean.

Preamble

-- Generated from ChapterNavierStokesFockManyMode.lean — theorem BookProof.NavierStokesFlow.FockManyMode.commForm_fockH
import Mathlib
import Definitions.Def_ChapterNavierStokesFockManyMode
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesShiftHamiltonian
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.DirectSumEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.ShiftHamiltonian.ShiftData
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.FockManyMode

variable {d : ℕ} {κ : Fin d → ℝ}


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato ShiftHamiltonian

Formal statement

theorem BookProof.NavierStokesFlow.FockManyMode.commForm_fockH (hκ : ∀ i, 0 ≤ κ i) (x : maxDom (fockSym κ)) :
    commForm (fockH hκ) (diagMax (fockSym κ)) x
      = ∑ i, commForm (ShiftData.shiftH (modeData hκ i)) (diagMax (fockSym κ)) x := by sorry

Source

https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterNavierStokesFlow.lean

View graph