Theorems · Theorem · real analysis
CauSeq.limZero_congr
∀ {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} [inst_4 : IsAbsoluteValue abv] {f g : CauSeq β abv}, f ≈ g → (f.LimZero ↔ g.LimZero)- Defined in
- Mathlib.Algebra.Order.CauSeq.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- sub_add_cancelproof · cited by 344
- CauSeqstatement and proof · cited by 189
- IsAbsoluteValuestatement and proof · cited by 160
- CauSeq.LimZerostatement and proof · cited by 46
- CauSeq.add_limZeroproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- CauSeq.lim_eq_zero_iffproof · cited by 1
- CauSeq.lim_invproof · cited by 0