Theorems · Definition · real analysis
CauSeq.Pos
{α : Type u_1} → [inst : Field α] → [inst_1 : LinearOrder α] → [inst_2 : IsStrictOrderedRing α] → CauSeq α abs → PropThe entries of a positive Cauchy sequence eventually have a positive lower bound.
- Defined in
- Mathlib.Algebra.Order.CauSeq.Basic
- Cited by
- 13 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
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- absstatement and proof · cited by 1,814
- CauSeqstatement and proof · cited by 189
Cited by13
Results whose statement or proof uses this declaration.
- CauSeq.const_ltproof · cited by 5
- CauSeq.lt_totalproof · cited by 3
- CauSeq.lt_of_eq_of_ltproof · cited by 2
- CauSeq.lt_of_lt_of_eqproof · cited by 2
- CauSeq.pos_add_limZerostatement and proof · cited by 2
- CauSeq.const_posstatement and proof · cited by 1
- CauSeq.exists_ltproof · cited by 1
- CauSeq.lt_transproof · cited by 1
- CauSeq.not_limZero_of_posstatement and proof · cited by 1
- CauSeq.add_posstatement and proof · cited by 1
- CauSeq.trichotomystatement and proof · cited by 1
- CauSeq.mul_posstatement and proof · cited by 0