Theorems · Definition · real analysis
CauSeq.LimZero
{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} → CauSeq β abv → PropLimZero f holds when f approaches 0.
- Defined in
- Mathlib.Algebra.Order.CauSeq.Basic
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 47 from the axioms · 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
- CauSeqstatement and proof · cited by 189
Cited by47
Results whose statement or proof uses this declaration.
- CauSeq.invstatement and proof · cited by 8
- CauSeq.abv_pos_of_not_limZerostatement and proof · cited by 6
- CauSeq.add_limZerostatement and proof · cited by 6
- CauSeq.const_limZerostatement and proof · cited by 6
- CauSeq.lim_negproof · cited by 6
- CauSeq.lim_addproof · cited by 5
- CauSeq.mul_limZero_rightstatement and proof · cited by 5
- CauSeq.neg_limZerostatement and proof · cited by 5
- CauSeq.mul_limZero_leftstatement and proof · cited by 4
- CauSeq.const_equivproof · cited by 3
- CauSeq.Completion.mk_eqstatement · cited by 3
- CauSeq.lt_totalproof · cited by 3