Theorems · Theorem · general topology
LipschitzWith.norm_le_mul
∀ {E : Type u_2} {F : Type u_3} [inst : SeminormedAddGroup E] [inst_1 : SeminormedAddGroup F] {f : E → F} {K : NNReal},
LipschitzWith K f → f 0 = 0 → ∀ (x : E), ‖f x‖ ≤ ↑K * ‖x‖- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 2 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.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- Dist.distproof · cited by 1,539
- NNReal.toRealstatement and proof · cited by 1,260
- SeminormedAddGroupstatement and proof · cited by 331
- LipschitzWithstatement and proof · cited by 316
- dist_zero_rightproof · cited by 172
- LipschitzWith.dist_le_mulproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.opNorm_le_iff_lipschitzproof · cited by 2
- LipschitzWith.nnorm_le_mulproof · cited by 0