Theorems · Theorem · logic and foundations
IsClub.sInter
∀ {α : Type v} [inst : LinearOrder α] [WellFoundedLT α] {s : Set (Set α)},
Order.cof α ≠ Cardinal.aleph0 → Cardinal.mk ↑s < Order.cof α → (∀ x ∈ s, IsClub x) → IsClub (⋂₀ s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderWellFoundedLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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
- LinearOrderstatement and proof · cited by 8,572
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Set.rangeproof · cited by 4,705
- LE.le.transproof · cited by 3,151
- Cardinalstatement · cited by 2,598
- SupSet.sSupproof · cited by 954
- Cardinal.mkstatement and proof · cited by 942
- LE.le.trans_ltproof · cited by 795
- IsEmptyproof · cited by 759
- BddAboveproof · cited by 620
Cited by2
Results whose statement or proof uses this declaration.
- IsClub.sInter_of_countableproof · cited by 2
- IsClub.iInterproof · cited by 1