Theorems · Theorem · general topology
ContractingWith.toLipschitzWith
∀ {α : Type u_1} [inst : EMetricSpace α] {K : NNReal} {f : α → α}, ContractingWith K f → LipschitzWith K f- Defined in
- Mathlib.Topology.MetricSpace.Contracting
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- LipschitzWithstatement · cited by 316
- EMetricSpacestatement and proof · cited by 242
- ContractingWithstatement and proof · cited by 39
Cited by4
Results whose statement or proof uses this declaration.
- ContractingWith.exists_fixedPointproof · cited by 4
- ContractingWith.dist_le_mulproof · cited by 1
- ContractingWith.isFixedPt_fixedPoint_iterateproof · cited by 1
- ContractingWith.apriori_dist_iterate_fixedPoint_leproof · cited by 0