Theorems · Theorem · order theory
sSupIndep_iff_finite
∀ {α : Type u_2} [inst : CompleteLattice α] [IsCompactlyGenerated α] {s : Set α},
sSupIndep s ↔ ∀ (t : Finset α), ↑t ⊆ s → sSupIndep ↑t- Defined in
- Mathlib.Order.CompactlyGenerated.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Bot.botproof · cited by 4,720
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupproof · cited by 954
- Set.Subset.transproof · cited by 218
- Set.mem_singletonproof · cited by 183
- Set.sdiff_subsetproof · cited by 156
- Finset.mem_insert_selfproof · cited by 128
- Finset.coe_insertproof · cited by 124
- disjoint_iffproof · cited by 76
Cited by1
Results whose statement or proof uses this declaration.
- sSupIndep_iUnion_of_directedproof · cited by 1