`BookProof.NavierStokesFlow.Carleman.tridiagOp_basis_zero` (c : ℕ → ℂ) : ((tridiagOp c (basis 0) : lpFiniteModes ℕ) : L2N) = (starRingEnd ℂ (c 0)) • lp.single 2 1 (1 : ℂ)

Proved

BookProof.NavierStokesFlow.Carleman.tridiagOp_basis_zero

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesCarleman.

BookProof.NavierStokesFlow.Carleman.tridiagOp_basis_zero (c : ℕ → ℂ) : ((tridiagOp c (basis 0) : lpFiniteModes ℕ) : L2N) = (starRingEnd ℂ (c 0)) • lp.single 2 1 (1 : ℂ)

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.Carleman.tridiagOp_basis_zero.

Preamble

-- Generated from ChapterNavierStokesCarleman.lean — theorem BookProof.NavierStokesFlow.Carleman.tridiagOp_basis_zero
import Mathlib
import Definitions.Def_ChapterNavierStokesCarleman
import Definitions.Def_ChapterNavierStokesDeficiency
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.JacobiDeficiency
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.Carleman


open scoped ENNReal



open LpNat DiagonalEsa FullEsa

Formal statement

theorem BookProof.NavierStokesFlow.Carleman.tridiagOp_basis_zero (c : ℕ → ℂ) :
    ((tridiagOp c (basis 0) : lpFiniteModes ℕ) : L2N)
      = (starRingEnd ℂ (c 0)) • lp.single 2 1 (1 : ℂ) := by sorry

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