Prove2Me

`BookProof.NavierStokesFlow.matrixFlow_vec_hasDerivAt` (A : Matrix (Fin n) (Fin n) ℂ) (x : Fin n → ℂ) (t : ℝ) : HasDerivAt (fun s : ℝ => matrixFlow A s *ᵥ x) (A *ᵥ (matrixFlow A t

Proved
BookProof.NavierStokesFlow.matrixFlow_vec_hasDerivAt

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesCauchy.

BookProof.NavierStokesFlow.matrixFlow_vec_hasDerivAt (A : Matrix (Fin n) (Fin n) ℂ) (x : Fin n → ℂ) (t : ℝ) : HasDerivAt (fun s : ℝ => matrixFlow A s *ᵥ x) (A *ᵥ (matrixFlow A t *ᵥ x)) t

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.matrixFlow_vec_hasDerivAt.

Preamble
-- Generated from ChapterNavierStokesCauchy.lean — theorem BookProof.NavierStokesFlow.matrixFlow_vec_hasDerivAt
import Mathlib
import Definitions.Def_ChapterNavierStokesCauchy
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow


open scoped BigOperators Matrix Matrix.Norms.Operator

variable {n : ℕ}
Formal statement
theorem BookProof.NavierStokesFlow.matrixFlow_vec_hasDerivAt (A : Matrix (Fin n) (Fin n) ℂ) (x : Fin n → ℂ) (t : ℝ) :
    HasDerivAt (fun s : ℝ => matrixFlow A s *ᵥ x) (A *ᵥ (matrixFlow A t *ᵥ x)) t := by sorry

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