Theorems · Definition · ordinary differential equations
ODE.FunSpace.compProj
{E : Type u_1} →
[inst : NormedAddCommGroup E] →
{tmin tmax : ℝ} → {t₀ : ↑(Set.Icc tmin tmax)} → {x₀ : E} → {r L : NNReal} → ODE.FunSpace t₀ x₀ r L → ℝ → EExtend the domain of α from Icc tmin tmax to ℝ such that α t = α tmin for all t ≤ tmin
and α t = α tmax for all t ≥ tmax.
- Defined in
- Mathlib.Analysis.ODE.PicardLindelof
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.Elemstatement and proof · cited by 7,166
- NNRealstatement and proof · cited by 4,310
- Set.Iccstatement and proof · cited by 1,702
- Set.projIccproof · cited by 56
- ODE.FunSpacestatement and proof · cited by 37
- ODE.FunSpace.toFunproof · cited by 20
Cited by14
Results whose statement or proof uses this declaration.
- ODE.FunSpace.nextproof · cited by 16
- ODE.FunSpace.next_applystatement · cited by 5
- ODE.FunSpace.compProj_applystatement · cited by 3
- ODE.FunSpace.compProj_of_memstatement · cited by 3
- ODE.FunSpace.continuous_compProjstatement · cited by 3
- ODE.FunSpace.compProj_mem_closedBallstatement · cited by 2
- ODE.FunSpace.compProj_valstatement · cited by 2
- IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAtproof · cited by 2
- ODE.FunSpace.intervalIntegrable_comp_compProjstatement · cited by 1
- ODE.FunSpace.continuousOn_comp_compProjstatement · cited by 1
- ODE.FunSpace.dist_iterate_next_apply_leproof · cited by 1