Theorems · Theorem · sequences and series
dist_le_tsum_dist_of_tendsto
∀ {α : Type u_1} [inst : PseudoMetricSpace α] {f : ℕ → α} {a : α},
(Summable fun n => dist (f n) (f n.succ)) →
Filter.Tendsto f Filter.atTop (nhds a) → ∀ (n : ℕ), dist (f n) a ≤ ∑' (m : ℕ), dist (f (n + m)) (f (n + m).succ)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- le_rflproof · cited by 1,558
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- tsumstatement and proof · cited by 1,148
- Summablestatement and proof · cited by 778
- dist_le_tsum_of_dist_le_of_tendstoproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- dist_le_tsum_dist_of_tendsto₀proof · cited by 0