`BookProof.NavierStokesEulerian.dirDeriv_coord` (k j : Fin 3) (x : Fin 3 → ℝ) : dirDeriv (fun y => y k) j x = if k = j then 1 else 0

Proved

BookProof.NavierStokesEulerian.dirDeriv_coord

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesEulerian.

BookProof.NavierStokesEulerian.dirDeriv_coord (k j : Fin 3) (x : Fin 3 → ℝ) : dirDeriv (fun y => y k) j x = if k = j then 1 else 0

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

Preamble

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



open BookProof.NavierStokesFlow Matrix

Formal statement

theorem BookProof.NavierStokesEulerian.dirDeriv_coord (k j : Fin 3) (x : Fin 3 → ℝ) :
    dirDeriv (fun y => y k) j x = if k = j then 1 else 0 := by sorry

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