Theorems · Theorem · general topology
lipschitzWith_iff_norm_neg_add_le
∀ {E : Type u_2} {F : Type u_3} [inst : SeminormedAddGroup E] [inst_1 : SeminormedAddGroup F] {f : E → F} {C : NNReal},
LipschitzWith C f ↔ ∀ (x y : E), ‖-f x + f y‖ ≤ ↑C * ‖-x + y‖- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
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 · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement and proof · cited by 1,260
- SeminormedAddGroupstatement and proof · cited by 331
- LipschitzWithstatement · cited by 316
- dist_eq_norm_neg_addproof · cited by 46
- lipschitzWith_iff_dist_le_mulproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- LipschitzWith.norm_neg_add_leproof · cited by 1