`BookProof.NavierStokesEulerian.cyclicShear_divergence_free` (x : Fin 3 → ℝ) : ∑ j : Fin 3, dirDeriv (fun y => cyclicShear y j) j x = 0

Proved

BookProof.NavierStokesEulerian.cyclicShear_divergence_free

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesEulerian.

BookProof.NavierStokesEulerian.cyclicShear_divergence_free (x : Fin 3 → ℝ) : ∑ j : Fin 3, dirDeriv (fun y => cyclicShear y j) j x = 0

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

Preamble

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



open BookProof.NavierStokesFlow Matrix

Formal statement

theorem BookProof.NavierStokesEulerian.cyclicShear_divergence_free (x : Fin 3 → ℝ) :
    ∑ j : Fin 3, dirDeriv (fun y => cyclicShear y j) j x = 0 := by sorry

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