Theorems · Theorem · general topology
AntilipschitzWith.le_mul_norm
∀ {E : Type u_2} {F : Type u_3} [inst : SeminormedAddGroup E] [inst_1 : SeminormedAddGroup F] {f : E → F} {K : NNReal},
AntilipschitzWith K f → f 0 = 0 → ∀ (x : E), ‖x‖ ≤ ↑K * ‖f x‖- Defined in
- Mathlib.Analysis.Normed.Group.Uniform
- Cited by
- 2 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.
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
- dist_zero_rightproof · cited by 172
- AntilipschitzWithstatement and proof · cited by 132
- AntilipschitzWith.le_mul_distproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- AntilipschitzWith.le_mul_nnnormproof · cited by 1
- antilipschitzWith_iff_exists_mul_le_normproof · cited by 1