Theorems · Theorem · order theory
lt_csSup_iff
∀ {α : Type u_1} [inst : ConditionallyCompleteLinearOrder α] {s : Set α} {a : α},
BddAbove s → s.Nonempty → (a < sSup s ↔ ∃ b ∈ s, a < b)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- isLUB_csSupproof · cited by 34
- lt_isLUB_iffproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- IsClosed.Icc_subset_of_forall_mem_nhdsGT_of_Icc_subsetproof · cited by 2
- Order.IsNormal.preimage_Iicproof · cited by 2
- Ordinal.IsPrincipal.sSupproof · cited by 2
- lt_ciSup_iffproof · cited by 0