Theorems · Theorem · order theory
CompleteLattice.isCompactElement_finsetSup
∀ {α : Type u_3} {β : Type u_4} [inst : CompleteLattice α] {f : β → α} (s : Finset β),
(∀ x ∈ s, IsCompactElement (f x)) → IsCompactElement (s.sup f)- Defined in
- Mathlib.Order.CompactlyGenerated.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- Set.Nonemptyproof · cited by 2,627
- CompleteLatticestatement and proof · cited by 1,048
- le_transproof · cited by 985
- SupSet.sSupproof · cited by 954
- Finset.imageproof · cited by 910
- Finset.supstatement and proof · cited by 530
- DirectedOnproof · cited by 271
- Finset.le_supproof · cited by 112
- Finset.mem_imageproof · cited by 105
- IsCompactElementstatement and proof · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- Submodule.fg_iff_compactproof · cited by 1
- IntermediateField.adjoin_finset_isCompactElementproof · cited by 1
- Submodule.finset_span_isCompactElementproof · cited by 1