Theorems · Theorem · general topology
IsCompactSystem.insert_univ
∀ {α : Type u_1} {S : Set (Set α)}, IsCompactSystem S → IsCompactSystem (insert Set.univ S)Inserting univ into a compact system gives a compact system.
- Cited by
- 2 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.
Cites15
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
- Set.univstatement and proof · cited by 3,945
- LE.le.transproof · cited by 3,151
- Set.Nonemptyproof · cited by 2,627
- Set.extproof · cited by 2,266
- Set.iInterproof · cited by 1,084
- IsEmptyproof · cited by 759
- isEmpty_or_nonemptyproof · cited by 269
- Nat.findproof · cited by 139
- Set.subset_empty_iffproof · cited by 40
- Set.iInter_univproof · cited by 24
- Set.dissipateproof · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- isCompactSystem_insert_univ_iffproof · cited by 0
- isCompactSystem_insert_univ_isCompact_isClosedproof · cited by 0