Theorems · Theorem · general topology
Filter.NeBot.nonempty_of_mem
∀ {α : Type u} {f : Filter α}, f.NeBot → ∀ {s : Set α}, s ∈ f → s.Nonempty- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Filterstatement and proof · cited by 8,121
- Set.Nonemptystatement · cited by 2,627
- Filter.NeBotstatement and proof · cited by 853
- Filter.nonempty_of_memproof · cited by 36
Cited by18
Results whose statement or proof uses this declaration.
- uniformContinuous_uniformly_extendproof · cited by 6
- CauchyFilter.denseRange_pureCauchyproof · cited by 5
- SequentiallyComplete.seq_memproof · cited by 2
- Filter.totallyBounded_iff_filterproof · cited by 2
- IsSelfAdjoint.isConnected_spectrum_complproof · cited by 1
- Filter.mul_eq_one_iffproof · cited by 1
- exists_seq_infinite_isOpen_pairwise_disjointproof · cited by 1
- DiscreteUniformity.eq_pure_of_cauchyproof · cited by 1
- Filter.add_eq_zero_iffproof · cited by 1
- Filter.NeBot.zero_div_nonnegproof · cited by 0
- Filter.NeBot.zero_mul_nonnegproof · cited by 0
- Filter.NeBot.zero_smul_nonnegproof · cited by 0