Theorems · Theorem · general topology
ContractingWith.dist_inequality
∀ {α : Type u_1} [inst : MetricSpace α] {K : NNReal} {f : α → α},
ContractingWith K f → ∀ (x y : α), dist x y ≤ (dist x (f x) + dist y (f y)) / (1 - ↑K)- Defined in
- Mathlib.Topology.MetricSpace.Contracting
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- one_mulproof · cited by 2,841
- mul_commproof · cited by 2,262
- le_reflproof · cited by 2,061
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement and proof · cited by 1,539
- NNReal.toRealstatement and proof · cited by 1,260
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
- sub_mulproof · cited by 170
- le_div_iff₀proof · cited by 75
Cited by1
Results whose statement or proof uses this declaration.
- ContractingWith.dist_le_of_fixedPointproof · cited by 2