Theorems · Theorem · functional analysis
NormedAddGroupHom.antilipschitz_of_norm_ge
∀ {V₁ : Type u_2} {V₂ : Type u_3} [inst : SeminormedAddCommGroup V₁] [inst_1 : SeminormedAddCommGroup V₂]
(f : NormedAddGroupHom V₁ V₂) {K : NNReal}, (∀ (x : V₁), ‖x‖ ≤ ↑K * ‖f x‖) → AntilipschitzWith K ⇑f- Defined in
- Mathlib.Analysis.Normed.Group.Hom
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNReal.toRealstatement and proof · cited by 1,260
- map_subproof · cited by 565
- NormedAddGroupHomstatement and proof · cited by 216
- dist_eq_normproof · cited by 182
- AntilipschitzWithstatement · cited by 132
- AntilipschitzWith.of_le_mul_distproof · cited by 12
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