Theorems · Theorem · real analysis
CauSeq.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 : CauSeq β abv), ∃ r, ∀ (i : ℕ), abv (↑f i) < r- Defined in
- Mathlib.Algebra.Order.CauSeq.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- CauSeqstatement and proof · cited by 189
- IsAbsoluteValuestatement and proof · cited by 160
- IsCauSeqstatement · cited by 91
- IsCauSeq.boundedproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- CauSeq.exists_gtproof · cited by 2