Theorems · Theorem · general topology
ContractingWith.dist_fixedPoint_le
∀ {α : Type u_1} [inst : MetricSpace α] {K : NNReal} {f : α → α} (hf : ContractingWith K f) [inst_1 : Nonempty α]
[inst_2 : CompleteSpace α] (x : α), dist x (ContractingWith.fixedPoint f hf) ≤ dist x (f x) / (1 - ↑K)- Defined in
- Mathlib.Topology.MetricSpace.Contracting
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- CompleteSpacestatement and proof · cited by 2,532
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement · cited by 1,539
- NNReal.toRealstatement · cited by 1,260
- ContractingWithstatement and proof · cited by 39
- ContractingWith.fixedPointstatement · cited by 9
- ContractingWith.fixedPoint_isFixedPtproof · cited by 4
- ContractingWith.dist_le_of_fixedPointproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ContractingWith.aposteriori_dist_iterate_fixedPoint_leproof · cited by 1