Theorems · Theorem · general topology
cauchySeq_shift
∀ {α : Type u} [uniformSpace : UniformSpace α] {u : ℕ → α} (k : ℕ), (CauchySeq fun n => u (n + k)) ↔ CauchySeq uAny shift of a Cauchy sequence is also a Cauchy sequence.
- Defined in
- Mathlib.Topology.UniformSpace.Cauchy
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpace
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.
- Setproof · cited by 53,352
- UniformSpacestatement and proof · cited by 2,040
- uniformityproof · cited by 765
- CauchySeqstatement and proof · cited by 131
- Filter.tendsto_add_atTop_natproof · cited by 19
- cauchySeq_iffproof · cited by 3
- CauchySeq.comp_tendstoproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Monotone.cauchySeq_series_mul_of_tendsto_zero_of_boundedproof · cited by 2