Theorems · Theorem · general topology
Filter.le_pure_iff
∀ {α : Type u_1} {f : Filter α} {a : α}, f ≤ pure a ↔ {a} ∈ f- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, 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 · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Filter.le_principal_iffproof · cited by 87
- Filter.principal_singletonproof · cited by 31
Cited by11
Results whose statement or proof uses this declaration.
- nhds_trueproof · cited by 2
- Ultrafilter.eq_pure_of_finite_memproof · cited by 2
- Filter.add_eq_zero_iffproof · cited by 1
- DiscreteUniformity.eq_pure_of_cauchyproof · cited by 1
- Filter.Subsingleton.exists_eq_pureproof · cited by 1
- Filter.mul_eq_one_iffproof · cited by 1
- nhdsWithin_of_mem_discreteproof · cited by 0
- Filter.le_one_iffproof · cited by 0
- Filter.nonpos_iffproof · cited by 0
- Filter.NeBot.eq_pure_iffproof · cited by 0
- SummationFilter.eq_unconditional_of_finiteproof · cited by 0