Theorems · Definition · real analysis
CauSeq
{α : Type u_3} →
[inst : Field α] → [inst_1 : LinearOrder α] → [IsStrictOrderedRing α] → (β : Type u_4) → [Ring β] → (β → α) → Type u_4CauSeq β abv is the type of β-valued Cauchy sequences, with respect to the absolute value
function abv.
- Defined in
- Mathlib.Algebra.Order.CauSeq.Basic
- Cited by
- 189 results in Mathlib
- Foundations
- Depth 46 from the axioms, rests on 480 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsStrictOrderedRingstatement and proof · cited by 2,490
- IsCauSeqproof · cited by 91
Cited by210
Results whose statement or proof uses this declaration.
- CauSeq.conststatement · cited by 58
- CauSeq.LimZerostatement and proof · cited by 46
- CauSeq.limstatement and proof · cited by 35
- PadicSeqproof · cited by 30
- Padic.valuationproof · cited by 28
- CauSeq.Completion.mkstatement · cited by 24
- Real.mkstatement and proof · cited by 19
- CauSeq.equiv_limstatement and proof · cited by 15
- CauSeq.Posstatement and proof · cited by 13
- Complex.exp'statement · cited by 9
- Padic.norm_eq_zpow_neg_valuationproof · cited by 9
- CauSeq.le_of_existsstatement and proof · cited by 9
Showing the 200 most cited of 210.