Prove2Me

(x : lpFiniteModes ℕ) (k : ℕ) : (((cre (cre x) : lpFiniteModes ℕ) : L2I ℕ) : ℕ → ℂ) (k + 2) = (Real.sqrt ((k : ℝ) + 2) : ℂ) * (Real.sqrt ((k : ℝ) + 1) : ℂ) * ((x : L2I ℕ) : ℕ → ℂ) k

Proved
BookProof.NavierStokesFlow.HermiteCanonical.cre_cre_coe_add_two

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

navier-stokesoperator-algebrastimepiece

Lean 4 theorem BookProof.NavierStokesFlow.HermiteCanonical.cre_cre_coe_add_two (module BookProof.NavierStokesFlow), source chapter BookProof/ChapterNavierStokesFlow.lean.

Preamble
-- Generated from ChapterNavierStokesHermiteCanonical.lean — theorem BookProof.NavierStokesFlow.HermiteCanonical.cre_cre_coe_add_two
import Mathlib
import Definitions.Def_ChapterNavierStokesHermiteCanonical
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.HermiteCanonical







open scoped ENNReal



open BookProof.NavierStokesFlow.LpNat BookProof.FarisLavine BookProof.NavierStokesFlow.IkebeKato BookProof.NavierStokesFlow.HermiteFarisLavine
Formal statement
theorem BookProof.NavierStokesFlow.HermiteCanonical.cre_cre_coe_add_two (x : lpFiniteModes ℕ) (k : ℕ) :
    (((cre (cre x) : lpFiniteModes ℕ) : L2I ℕ) : ℕ → ℂ) (k + 2)
      = (Real.sqrt ((k : ℝ) + 2) : ℂ) * (Real.sqrt ((k : ℝ) + 1) : ℂ)
        * ((x : L2I ℕ) : ℕ → ℂ) k := by sorry
Source
https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterNavierStokesFlow.lean

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