Theorems · Theorem · general topology
AntilipschitzWith.injective
∀ {α : Type u_4} {β : Type u_5} [inst : EMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {f : α → β},
AntilipschitzWith K f → Function.Injective f- Cited by
- 8 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement and proof · cited by 4,310
- MulZeroClass.mul_zeroproof · cited by 2,091
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealproof · cited by 1,279
- EDist.edistproof · cited by 735
- EMetricSpacestatement and proof · cited by 242
- AntilipschitzWithstatement and proof · cited by 132
- PseudoEMetricSpace.edist_selfproof · cited by 50
Cited by8
Results whose statement or proof uses this declaration.
- Isometry.injectiveproof · cited by 11
- AntilipschitzWith.isUniformEmbeddingproof · cited by 6
- LinearMap.injective_iff_antilipschitzproof · cited by 2
- ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitzproof · cited by 1
- LinearIndependent.eventuallyproof · cited by 1
- ApproximatesLinearOn.injectiveproof · cited by 1
- Dilation.injectiveproof · cited by 0
- IsCoercive.ker_eq_botproof · cited by 0