Theorems · Definition · ordinary differential equations
IsIntegralCurveOn
{E : Type u_1} → [inst : NormedAddCommGroup E] → [NormedSpace ℝ E] → (ℝ → E) → (ℝ → E → E) → Set ℝ → PropIsIntegralCurveOn γ v s means γ t is tangent to v t (γ t) within s for all t ∈ s.
- Defined in
- Mathlib.Analysis.ODE.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- HasDerivWithinAtproof · cited by 333
Cited by23
Results whose statement or proof uses this declaration.
- isIntegralCurveAt_iff_exists_mem_nhdsstatement and proof · cited by 5
- IsIntegralCurveOn.comp_mulstatement and proof · cited by 3
- isIntegralCurveOn_comp_addstatement and proof · cited by 3
- IsIntegralCurveOn.comp_addstatement and proof · cited by 2
- isIntegralCurveAt_comp_addproof · cited by 2
- isIntegralCurveOn_univstatement and proof · cited by 2
- IsIntegralCurveOn.continuousWithinAtstatement and proof · cited by 1
- IsIntegralCurveOn.isIntegralCurveAtstatement and proof · cited by 1
- IsIntegralCurveAt.comp_mul_ne_zeroproof · cited by 1
- isIntegralCurveAt_iff_exists_posstatement and proof · cited by 1
- isIntegralCurveOn_comp_substatement and proof · cited by 1
- isIntegralCurve_comp_addproof · cited by 1