Theorems · Theorem · order theory
Set.Finite.csSup_lt_iff
∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrder α] {s : Set α} {a : α},
s.Finite → s.Nonempty → (sSup s < a ↔ ∀ x ∈ s, x < a)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Set.Nonemptystatement and proof · cited by 2,627
- Set.Finitestatement and proof · cited by 1,814
- SupSet.sSupstatement and proof · cited by 954
- LE.le.trans_ltproof · cited by 795
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- le_csSupproof · cited by 66
- Set.Finite.bddAboveproof · cited by 19
- Set.Nonempty.csSup_memproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- norm_root_le_spectralValueproof · cited by 3
- Set.Finite.lt_csInf_iffproof · cited by 0