Theorems · Theorem · ordinary differential equations

IsIntegralCurveAt.isIntegralCurveOn

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {γ : ℝ → E} {v : ℝ → E → E} {s : Set ℝ},
  (∀ t ∈ s, IsIntegralCurveAt γ v t) → IsIntegralCurveOn γ v s

If γ is an integral curve at each t ∈ s, it is an integral curve on s.

Defined in

Mathlib.Analysis.ODE.Basic

Cited by

1 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace