Theorems · Theorem · real analysis
CauSeq.not_limZero_of_not_congr_zero
∀ {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 : CauSeq β abv}, ¬f ≈ 0 → ¬f.LimZero- Defined in
- Mathlib.Algebra.Order.CauSeq.Basic
- Cited by
- 3 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.
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
- sub_zeroproof · cited by 938
- CauSeqstatement and proof · cited by 189
- IsAbsoluteValuestatement and proof · cited by 160
- CauSeq.LimZerostatement and proof · cited by 46
Cited by3
Results whose statement or proof uses this declaration.
- Padic.norm_eq_zpow_neg_valuationproof · cited by 9
- PadicSeq.norm_eq_zpow_neg_valuationproof · cited by 2
- PadicSeq.stationaryproof · cited by 1