Theorems · Theorem · logic and foundations
IsClub.sInter_of_orderTop
∀ {α : Type v} [inst : LinearOrder α] {s : Set (Set α)} [OrderTop α], (∀ x ∈ s, IsClub x) → IsClub (⋂₀ s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- OrderTopstatement and proof · cited by 493
- Set.sInterstatement · cited by 225
- IsClubstatement and proof · cited by 30
- Set.mem_sInterproof · cited by 7
- IsClub.isCofinalproof · cited by 7
- IsClub.dirSupClosedproof · cited by 4
- DirSupClosed.sInterproof · cited by 3
- IsCofinal.top_memproof · cited by 2
- isCofinal_iff_top_memproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsClub.sInter_of_cof_le_oneproof · cited by 3
- IsClub.iInter_of_orderTopproof · cited by 0