Theorems · Theorem · general topology
Filter.mem_generate_of_mem
∀ {α : Type u} {s : Set (Set α)} {U : Set α}, U ∈ s → U ∈ Filter.generate s- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 5 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.generatestatement · cited by 30
Cited by5
Results whose statement or proof uses this declaration.
- Filter.atBot_eq_generate_of_forall_exists_leproof · cited by 1
- Filter.atTop_eq_generate_of_forall_exists_leproof · cited by 1
- Filter.map_generate_le_generate_preimage_preimageproof · cited by 0
- Filter.generate_image_preimage_le_comapproof · cited by 0
- Filter.generate_singletonproof · cited by 0