Theorems · Theorem · global analysis

IsMIntegralCurveAt.eventually_hasDerivAt

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {H : Type u_2} [inst_2 : TopologicalSpace H]
  {I : ModelWithCorners ℝ E H} {M : Type u_3} [inst_3 : TopologicalSpace M] [inst_4 : ChartedSpace H M] {γ : ℝ → M}
  {v : (x : M) → TangentSpace I x} {t₀ : ℝ} [inst_5 : IsManifold I 1 M],
  IsMIntegralCurveAt γ v t₀ →
    ∀ᶠ (t : ℝ) in nhds t₀,
      HasDerivAt (↑(extChartAt I (γ t₀)) ∘ γ) ((tangentCoordChange I (γ t) (γ t₀) (γ t)) (v (γ t))) t

Defined in

Mathlib.Geometry.Manifold.IntegralCurve.Basic

Cited by

1 results in Mathlib

Foundations

Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceIsManifold