Theorems · Theorem · general topology
MonoidHomClass.antilipschitz_of_bound
∀ {𝓕 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : SeminormedGroup E] [inst_1 : SeminormedGroup F]
[inst_2 : FunLike 𝓕 E F] [MonoidHomClass 𝓕 E F] (f : 𝓕) {K : NNReal},
(∀ (x : E), ‖x‖ ≤ ↑K * ‖f x‖) → AntilipschitzWith K ⇑f- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- FunLikestatement and proof · cited by 2,560
- NNReal.toRealstatement and proof · cited by 1,260
- map_mulproof · cited by 1,137
- SeminormedGroupstatement and proof · cited by 250
- MonoidHomClassstatement and proof · cited by 244
- AntilipschitzWithstatement · cited by 132
- map_invproof · cited by 95
- dist_eq_norm_inv_mulproof · cited by 41
Cited by1
Results whose statement or proof uses this declaration.
- antilipschitzWith_iff_exists_mul_le_norm'proof · cited by 0