Theorems · Theorem · real analysis
IsCauSeq.bounded
∀ {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 abv f → ∃ r, ∀ (i : ℕ), abv (f i) < r- Defined in
- Mathlib.Algebra.Order.CauSeq.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- LE.le.transproof · cited by 3,151
- IsStrictOrderedRingstatement and proof · cited by 2,490
- le_rflproof · cited by 1,558
- LE.le.trans_ltproof · cited by 795
- zero_lt_oneproof · cited by 598
- le_totalproof · cited by 294
- le_max_leftproof · cited by 215
- add_sub_cancelproof · cited by 195
- IsAbsoluteValuestatement and proof · cited by 160
Cited by3
Results whose statement or proof uses this declaration.
- IsCauSeq.bounded'proof · cited by 2
- CauSeq.boundedproof · cited by 1
- cauchy_productproof · cited by 1