Theorems · Theorem · order theory
sSup_mem_of_not_isSuccPrelimit
∀ {α : Type u_2} [inst : CompleteLinearOrder α] {s : Set α}, ¬Order.IsSuccPrelimit (sSup s) → sSup s ∈ s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- SupSet.sSupstatement and proof · cited by 954
- CovByproof · cited by 290
- Order.IsSuccPrelimitstatement and proof · cited by 157
- CompleteLinearOrderstatement and proof · cited by 126
- le_sSupproof · cited by 79
- CovBy.ltproof · cited by 51
- eq_of_le_of_not_ltproof · cited by 28
- not_forall_notproof · cited by 11
- lt_sSup_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- exists_eq_iSup_of_not_isSuccPrelimitproof · cited by 0