`BookProof.NavierStokesFlow.matrixFlow_cauchy_existsUnique` (A : Matrix (Fin n) (Fin n) ℂ) (x : Fin n → ℂ) : ∃! y : ℝ → Fin n → ℂ, y 0 = x ∧ ∀ t, HasDerivAt y (A *ᵥ y t) t

Proved

BookProof.NavierStokesFlow.matrixFlow_cauchy_existsUnique

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesCauchy.

BookProof.NavierStokesFlow.matrixFlow_cauchy_existsUnique (A : Matrix (Fin n) (Fin n) ℂ) (x : Fin n → ℂ) : ∃! y : ℝ → Fin n → ℂ, y 0 = x ∧ ∀ t, HasDerivAt y (A *ᵥ y t) t

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

Preamble

-- Generated from ChapterNavierStokesCauchy.lean — theorem BookProof.NavierStokesFlow.matrixFlow_cauchy_existsUnique
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_cauchy_existsUnique (A : Matrix (Fin n) (Fin n) ℂ) (x : Fin n → ℂ) :
    ∃! y : ℝ → Fin n → ℂ, y 0 = x ∧ ∀ t, HasDerivAt y (A *ᵥ y t) t := by sorry

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