Theorems · Theorem · order theory
Order.IsSuccPrelimit.isLUB_Iio
∀ {α : Type u_1} {a : α} [inst : LinearOrder α], Order.IsSuccPrelimit a → IsLUB (Set.Iio a) a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 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.
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
- le_of_ltproof · cited by 1,175
- Set.Iiostatement and proof · cited by 1,166
- LT.lt.trans_leproof · cited by 678
- IsLUBstatement · cited by 280
- upperBoundsproof · cited by 263
- Order.IsSuccPrelimitstatement and proof · cited by 157
- le_of_forall_ltproof · cited by 25
- Order.IsSuccPrelimit.lt_iff_exists_ltproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Order.IsSuccPrelimit.sSup_Iioproof · cited by 4
- Order.IsSuccLimit.isLUB_Iioproof · cited by 2
- Order.isLUB_Iio_iff_isSuccPrelimitproof · cited by 0