Theorems · Theorem · ordinary differential equations
ODE.FunSpace.range_toContinuousMap
∀ {E : Type u_1} [inst : NormedAddCommGroup E] {tmin tmax : ℝ} {t₀ : ↑(Set.Icc tmin tmax)} {x₀ : E} {r L : NNReal},
(Set.range fun α => ODE.FunSpace.toContinuousMap α) = {α | LipschitzWith L ⇑α ∧ α t₀ ∈ Metric.closedBall x₀ ↑r}- Defined in
- Mathlib.Analysis.ODE.PicardLindelof
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- Set.rangestatement and proof · cited by 4,705
- NNRealstatement and proof · cited by 4,310
- ContinuousMapstatement and proof · cited by 2,491
- Set.extproof · cited by 2,266
- Set.Iccstatement and proof · cited by 1,702
- NNReal.toRealstatement and proof · cited by 1,260
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