Theorems · Theorem · ordinary differential equations

IsPicardLindelof.continuousOn_uncurry

∀ {E : Type u_1} [inst : NormedAddCommGroup E] {f : ℝ → E → E} {tmin tmax : ℝ} {t₀ : ↑(Set.Icc tmin tmax)} {x₀ : E}
  {a r L K : NNReal},
  IsPicardLindelof f t₀ x₀ a r L K → ContinuousOn (Function.uncurry f) (Set.Icc tmin tmax ×ˢ Metric.closedBall x₀ ↑a)

Defined in: Mathlib.Analysis.ODE.PicardLindelof
Cited by: 2 results in Mathlib
Foundations: Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup

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Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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
NNRealstatement and proof · cited by 4,310
SProd.sprodstatement · cited by 1,750
Set.Iccstatement and proof · cited by 1,702
ContinuousOnstatement · cited by 1,411
NNReal.toRealstatement · cited by 1,260
Metric.closedBallstatement · cited by 704
IsPicardLindelofstatement and proof · cited by 33
IsPicardLindelof.lipschitzOnWithproof · cited by 5

Cited by2

Results whose statement or proof uses this declaration.

IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWithproof · cited by 2
IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAtproof · cited by 2