Theorems · Theorem · logic and foundations
IsClub.iInter_of_orderTop
∀ {α : Type v} [inst : LinearOrder α] {ι : Type u_1} {f : ι → Set α} [OrderTop α],
(∀ (i : ι), IsClub (f i)) → IsClub (⋂ i, f i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 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.
Cites7
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.iInterstatement · cited by 1,084
- OrderTopstatement and proof · cited by 493
- IsClubstatement and proof · cited by 30
- Set.sInter_rangeproof · cited by 16
- IsClub.sInter_of_orderTopproof · cited by 2
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