(i : Fin d) (x : lpFiniteModes (Occ d)) (α : Occ d) : (((cre i x : lpFiniteModes (Occ d)) : L2I (Occ d)) : Occ d → ℂ) α = (Real.sqrt (α i : ℝ) : ℂ) * ((x : L2I (Occ d)) : Occ d → ℂ) (dn i α)

Proved

BookProof.NavierStokesFlow.FockCanonical.cre_coe

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

navier-stokesoperator-algebrastimepiece

Lean 4 theorem BookProof.NavierStokesFlow.FockCanonical.cre_coe (module BookProof.NavierStokesFlow), source chapter BookProof/ChapterNavierStokesFlow.lean.

Preamble

-- Generated from ChapterNavierStokesFockCanonical.lean — theorem BookProof.NavierStokesFlow.FockCanonical.cre_coe
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}

Formal statement

theorem BookProof.NavierStokesFlow.FockCanonical.cre_coe (i : Fin d) (x : lpFiniteModes (Occ d)) (α : Occ d) :
    (((cre i x : lpFiniteModes (Occ d)) : L2I (Occ d)) : Occ d → ℂ) α
      = (Real.sqrt (α i : ℝ) : ℂ) * ((x : L2I (Occ d)) : Occ d → ℂ) (dn i α) := by sorry

Source

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

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