Theorems · Theorem · general topology
edist_le_range_sum_edist
∀ {α : Type u} [inst : PseudoEMetricSpace α] (f : ℕ → α) (n : ℕ),
edist (f 0) (f n) ≤ ∑ i ∈ Finset.range n, edist (f i) (f (i + 1))The triangle (polygon) inequality for sequences of points; Finset.range version.
- Defined in
- Mathlib.Topology.EMetricSpace.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 148 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- Finset.sumstatement · cited by 5,195
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Finset.rangestatement · cited by 1,341
- EDist.ediststatement · cited by 735
- Nat.Ico_zero_eq_rangeproof · cited by 25
- edist_le_Ico_sum_edistproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.