The Lean 4 theorem `secondDerivativeField_momentum` in the `ChapterNavierStokesFlow` chapter of the timepiece formalization
ProvedBookProof.NavierStokesFlow.secondDerivativeField_momentumtimepiece
The Lean 4 theorem secondDerivativeField_momentum in the ChapterNavierStokesFlow chapter of the timepiece formalization.
Preamble
-- Generated from ChapterNavierStokesFlow.lean — theorem BookProof.NavierStokesFlow.secondDerivativeField_momentum import Mathlib import Definitions.Def_ChapterNavierStokesFlow open BookProof.NavierStokesFlow open scoped BigOperators Matrix Kronecker ComplexOrder TensorProduct
Formal statement
theorem BookProof.NavierStokesFlow.secondDerivativeField_momentum (i j k l m n : Fin 3)
(p : MvPolynomial (Fin 3 × Fin 3 × Fin 3) ℂ) :
(MvPolynomial.pderiv (l, m, n)) (MvPolynomial.X (i, j, k) * p)
- MvPolynomial.X (i, j, k) * (MvPolynomial.pderiv (l, m, n)) p
= (if l = i ∧ m = j ∧ n = k then p else 0) := by sorrySource