Theorems · Theorem · general topology
LipschitzWith.add
∀ {α : Type u_4} {E : Type u_5} [inst : SeminormedAddCommGroup E] [inst_1 : PseudoEMetricSpace α] {Kf Kg : NNReal}
{f g : α → E}, LipschitzWith Kf f → LipschitzWith Kg g → LipschitzWith (Kf + Kg) fun x => f x + g x- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement and proof · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- PseudoEMetricSpacestatement and proof · cited by 1,536
- LipschitzWithstatement and proof · cited by 316
- LipschitzWith.lipschitzOnWithproof · cited by 16
- lipschitzOnWith_univproof · cited by 11
- LipschitzOnWith.addproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- LipschitzWith.ae_lineDifferentiableAtproof · cited by 3
- LipschitzWith.subproof · cited by 2
- ApproximatesLinearOn.lipschitzproof · cited by 1