Theorems · Theorem · general topology
MonoidHomClass.lipschitz_of_bound_nnnorm
∀ {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) (C : NNReal),
(∀ (x : E), ‖f x‖₊ ≤ C * ‖x‖₊) → LipschitzWith C ⇑f- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- NNRealstatement and proof · cited by 4,310
- FunLikestatement and proof · cited by 2,560
- NNReal.toRealproof · cited by 1,260
- NNNorm.nnnormstatement and proof · cited by 952
- LipschitzWithstatement · cited by 316
- SeminormedGroupstatement and proof · cited by 250
- MonoidHomClassstatement and proof · cited by 244
- Real.toNNReal_coeproof · cited by 36
- MonoidHomClass.lipschitz_of_boundproof · cited by 3
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