Theorems · Theorem · general topology
Filter.mem_iff_inf_principal_compl
∀ {α : Type u_1} {f : Filter α} {s : Set α}, s ∈ f ↔ f ⊓ Filter.principal sᶜ = ⊥- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Bot.botstatement · cited by 4,720
- Compl.complstatement and proof · cited by 2,925
- Set.Nonemptyproof · cited by 2,627
- Filter.principalstatement · cited by 740
- Filter.mem_of_supersetproof · cited by 308
- not_iff_notproof · cited by 159
- Filter.neBot_iffproof · cited by 27
- Set.inter_compl_selfproof · cited by 17
- Set.inter_compl_nonempty_iffproof · cited by 6
- Filter.inf_principal_neBot_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Filter.disjoint_principal_rightproof · cited by 10
- isOpen_singleton_iff_punctured_nhdsproof · cited by 1
- Filter.notMem_iff_inf_principal_complproof · cited by 1
- Filter.le_iff_forall_inf_principal_complproof · cited by 0