Theorems · Theorem · order theory
sSup_ne_top
∀ {α : Type u_5} [inst : CompleteLinearOrder α] [Nontrivial α] {s : Set α}, s.Finite → ⊤ ∉ s → sSup s ≠ ⊤- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Top.topstatement and proof · cited by 9,680
- Nontrivialstatement and proof · cited by 2,416
- Set.Finitestatement and proof · cited by 1,814
- SupSet.sSupstatement · cited by 954
- CompleteLinearOrderstatement and proof · cited by 126
- top_ne_botproof · cited by 15
- sSup_ne_of_notMemproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- sInf_ne_botproof · cited by 0