Theorems · Theorem · general topology
Filter.mem_principal
∀ {α : Type u_1} {s t : Set α}, s ∈ Filter.principal t ↔ t ⊆ s- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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 · cited by 8,121
- Filter.principalstatement · cited by 740
Cited by10
Results whose statement or proof uses this declaration.
- ContinuousWithinAt.tendsto_nhdsWithinproof · cited by 16
- TendstoUniformlyOn.monoproof · cited by 5
- TendstoUniformlyOn.tendsto_atproof · cited by 4
- derivedSet_monoproof · cited by 3
- Filter.Subsingleton.atTop_eqproof · cited by 3
- hasBasis_nhdsSet_Iic_Iioproof · cited by 2
- Filter.disjoint_principal_principalproof · cited by 1
- Filter.principal_eq_bot_iffproof · cited by 1
- UniformCauchySeqOn.monoproof · cited by 1
- pcontinuous_iff'proof · cited by 0