Theorems · Theorem · logic and foundations
IsClub.sInter_of_cof_le_one
∀ {α : Type v} [inst : LinearOrder α] {s : Set (Set α)}, Order.cof α ≤ 1 → (∀ x ∈ s, IsClub x) → IsClub (⋂₀ s)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
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.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Cardinalstatement · cited by 2,598
- IsEmptyproof · cited by 759
- OrderTopproof · cited by 493
- LT.lt.not_geproof · cited by 305
- isEmpty_or_nonemptyproof · cited by 269
- Set.sInterstatement and proof · cited by 225
- Order.cofstatement and proof · cited by 86
- NoTopOrderproof · cited by 50
- IsClubstatement and proof · cited by 30
- topOrderOrNoTopOrderproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- IsClub.sInter_of_countableproof · cited by 2
- IsClub.sInterproof · cited by 2
- IsClub.iInter_of_cof_le_oneproof · cited by 1