Theorems · Theorem · general topology
lipschitzOnWith_iff_norm_sub_le
∀ {E : Type u_2} {F : Type u_3} [inst : SeminormedAddCommGroup E] [inst_1 : SeminormedAddCommGroup F] {f : E → F}
{C : NNReal} {s : Set E}, LipschitzOnWith C f s ↔ ∀ ⦃x : E⦄, x ∈ s → ∀ ⦃y : E⦄, y ∈ s → ‖f x - f y‖ ≤ ↑C * ‖x - y‖- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNReal.toRealstatement and proof · cited by 1,260
- LipschitzOnWithstatement and proof · cited by 164
- norm_neg_addproof · cited by 12
- lipschitzOnWith_iff_norm_neg_add_leproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- LipschitzOnWith.norm_sub_leproof · cited by 7
- Convex.lipschitzOnWith_of_nnnorm_hasFDerivWithin_leproof · cited by 5
- HasStrictFDerivAt.exists_lipschitzOnWith_of_nnnorm_ltproof · cited by 2