∀ {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]
  [inst_5 : IsManifold I 1 M] {v : (x : M) → TangentSpace I x} (t₀ : ℝ) {x₀ : M} [CompleteSpace E]
  [BoundarylessManifold I M],
  ContMDiffAt I I.tangent 1 (fun x => { proj := x, snd := v x }) x₀ → ∃ γ, γ t₀ = x₀ ∧ IsMIntegralCurveAt γ v t₀