Theorems · Theorem · general topology
Filter.mem_inf_principal
∀ {α : Type u} {f : Filter α} {s t : Set α}, s ∈ f ⊓ Filter.principal t ↔ {x | x ∈ t → x ∈ s} ∈ f- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.ofPredstatement and proof · cited by 6,101
- Filter.principalstatement · cited by 740
Cited by9
Results whose statement or proof uses this declaration.
- Filter.eventually_inf_principalproof · cited by 18
- Filter.map_comapproof · cited by 10
- Filter.inf_principal_eq_botproof · cited by 3
- eventuallyEq_nhdsWithin_iffproof · cited by 3
- map_snd_nhdsWithinproof · cited by 2
- Units.isEmbedding_val_mk'proof · cited by 2
- IsCompact.compl_mem_sets_of_nhdsWithinproof · cited by 2
- AddUnits.isEmbedding_val_mk'proof · cited by 1
- map_fst_nhdsWithinproof · cited by 1