Theorems · Theorem · order theory
IsLUB.isSuccPrelimit_of_notMem
∀ {α : Type u_1} {a : α} [inst : LinearOrder α] {s : Set α}, IsLUB s a → a ∉ s → Order.IsSuccPrelimit a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 20 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.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- LE.le.antisymmproof · cited by 507
- CovByproof · cited by 290
- IsLUBstatement and proof · cited by 280
- Order.IsSuccPrelimitstatement · cited by 157
- CovBy.ltproof · cited by 51
- IsLUB.exists_betweenproof · cited by 8
- CovBy.ge_of_gtproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- IsLUB.isSuccLimit_of_notMemproof · cited by 2
- IsLUB.mem_of_not_isSuccPrelimitproof · cited by 0