Theorems · Theorem · real analysis
IsCauSeq.of_abv
∀ {α : Type u_1} {β : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [inst_2 : IsStrictOrderedRing α]
[inst_3 : Ring β] {abv : β → α} [IsAbsoluteValue abv] {f : ℕ → β},
(IsCauSeq abs fun m => ∑ n ∈ Finset.range m, abv (f n)) → IsCauSeq abv fun m => ∑ n ∈ Finset.range m, f n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Finset.sumstatement and proof · cited by 5,195
- IsStrictOrderedRingstatement and proof · cited by 2,490
- absstatement and proof · cited by 1,814
- le_rflproof · cited by 1,558
- Finset.rangestatement and proof · cited by 1,341
- IsAbsoluteValuestatement and proof · cited by 160
- IsCauSeqstatement and proof · cited by 91
- IsCauSeq.of_abv_leproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsCauSeq.geo_seriesproof · cited by 1
- Complex.isCauSeq_expproof · cited by 1