Theorems · Definition · ordinary differential equations
IsIntegralCurveAt
{E : Type u_1} → [inst : NormedAddCommGroup E] → [NormedSpace ℝ E] → (ℝ → E) → (ℝ → E → E) → ℝ → PropIsIntegralCurveAt γ v t₀ means γ : ℝ → E is a local integral curve of v in a neighbourhood
containing t₀.
- Defined in
- Mathlib.Analysis.ODE.Basic
- Cited by
- 15 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- nhdsproof · cited by 5,554
- Filter.Eventuallyproof · cited by 3,134
- HasDerivAtproof · cited by 493
Cited by15
Results whose statement or proof uses this declaration.
- isIntegralCurveAt_iff_exists_mem_nhdsstatement · cited by 5
- isIntegralCurveAt_comp_addstatement · cited by 2
- IsIntegralCurve.isIntegralCurveAtstatement · cited by 2
- IsIntegralCurveOn.isIntegralCurveAtstatement · cited by 1
- isIntegralCurveAt_comp_substatement and proof · cited by 1
- isIntegralCurveAt_iff_exists_posstatement · cited by 1
- IsIntegralCurveAt.comp_mul_ne_zerostatement and proof · cited by 1
- IsIntegralCurveAt.continuousAtstatement and proof · cited by 1
- IsIntegralCurveAt.isIntegralCurveOnstatement and proof · cited by 1
- isIntegralCurve_iff_isIntegralCurveAtstatement and proof · cited by 0
- isIntegralCurveAt_comp_mul_ne_zerostatement and proof · cited by 0
- isIntegralCurveOn_iff_isIntegralCurveAtstatement · cited by 0