Theorems · Theorem · general topology
LipschitzWith.edist_iterate_succ_le_geometric
∀ {α : Type u} [inst : PseudoEMetricSpace α] {K : NNReal} {f : α → α},
LipschitzWith K f → ∀ (x : α) (n : ℕ), edist (f^[n] x) (f^[n + 1] x) ≤ edist x (f x) * ↑K ^ n- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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.
- ENNRealstatement and proof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- mul_commproof · cited by 2,262
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- Nat.iteratestatement and proof · cited by 740
- EDist.ediststatement and proof · cited by 735
- LipschitzWithstatement and proof · cited by 316
- Function.iterate_succproof · cited by 19
- LipschitzWith.iterateproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- ContractingWith.exists_fixedPointproof · cited by 4