`BookProof.NavierStokesEulerian.eulerian_momentum_constraint` (j k : Fin 3) (p : MvPolynomial (Fin 3) ℂ) : (MvPolynomial.pderiv k) (MvPolynomial.X j * p) - MvPolynomial.X j * (MvPo

Proved

BookProof.NavierStokesEulerian.eulerian_momentum_constraint

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesEulerian.

BookProof.NavierStokesEulerian.eulerian_momentum_constraint (j k : Fin 3) (p : MvPolynomial (Fin 3) ℂ) : (MvPolynomial.pderiv k) (MvPolynomial.X j * p) - MvPolynomial.X j * (MvPolynomial.pderiv k) p = (if k = j then p else 0)

Formalization note: Lean 4 identifier BookProof.NavierStokesEulerian.eulerian_momentum_constraint.

Preamble

-- Generated from ChapterNavierStokesEulerian.lean — theorem BookProof.NavierStokesEulerian.eulerian_momentum_constraint
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Mathlib
import Definitions.Def_ChapterNavierStokesEulerian
open BookProof.NavierStokesEulerian



open BookProof.NavierStokesFlow Matrix

Formal statement

theorem BookProof.NavierStokesEulerian.eulerian_momentum_constraint (j k : Fin 3) (p : MvPolynomial (Fin 3) ℂ) :
    (MvPolynomial.pderiv k) (MvPolynomial.X j * p)
      - MvPolynomial.X j * (MvPolynomial.pderiv k) p = (if k = j then p else 0) := by sorry

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