Theorems · Theorem · general topology
Nat.hyperfilter_le_atTop
↑(Filter.hyperfilter ℕ) ≤ Filter.atTop
- Defined in
- Mathlib.Order.Filter.Ultrafilter.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Filterstatement · cited by 8,121
- Filter.atTopstatement · cited by 2,405
- LE.le.trans_eqproof · cited by 328
- Ultrafilter.toFilterstatement · cited by 172
- Nat.cofinite_eq_atTopproof · cited by 37
- Filter.hyperfilterstatement · cited by 30
- Filter.hyperfilter_le_cofiniteproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Hyperreal.coe_lt_omegaproof · cited by 2
- Hyperreal.lt_of_tendsto_zero_of_posproof · cited by 1
- Hyperreal.isSt_of_tendstoproof · cited by 1
- Hyperreal.infiniteNeg_of_tendsto_botproof · cited by 0
- Hyperreal.infinitePos_of_tendsto_topproof · cited by 0