`BookProof.NavierStokesEulerian.dirDeriv_eq` {f : (Fin 3 → ℝ) → ℝ} {L : (Fin 3 → ℝ) →L[ℝ] ℝ} {x : Fin 3 → ℝ} (hf : HasFDerivAt f L x) (j : Fin 3) : dirDeriv f j x = L (evec j)

Proved

BookProof.NavierStokesEulerian.dirDeriv_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesEulerian.

BookProof.NavierStokesEulerian.dirDeriv_eq {f : (Fin 3 → ℝ) → ℝ} {L : (Fin 3 → ℝ) →L[ℝ] ℝ} {x : Fin 3 → ℝ} (hf : HasFDerivAt f L x) (j : Fin 3) : dirDeriv f j x = L (evec j)

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

Preamble

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



open BookProof.NavierStokesFlow Matrix

Formal statement

theorem BookProof.NavierStokesEulerian.dirDeriv_eq {f : (Fin 3 → ℝ) → ℝ} {L : (Fin 3 → ℝ) →L[ℝ] ℝ} {x : Fin 3 → ℝ}
    (hf : HasFDerivAt f L x) (j : Fin 3) : dirDeriv f j x = L (evec j) := by sorry

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