Theorems · Theorem · order theory
Order.isLUB_Iio_iff_isSuccPrelimit
∀ {α : Type u_1} {a : α} [inst : LinearOrder α], IsLUB (Set.Iio a) a ↔ Order.IsSuccPrelimit a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.Iiostatement and proof · cited by 1,166
- Set.Iicproof · cited by 1,111
- CovByproof · cited by 290
- IsLUBstatement and proof · cited by 280
- Order.IsSuccPrelimitstatement · cited by 157
- LT.lt.falseproof · cited by 66
- CovBy.ltproof · cited by 51
- IsLUB.uniqueproof · cited by 21
- isLUB_Iicproof · cited by 3
- Order.IsSuccPrelimit.isLUB_Iioproof · cited by 3
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