Theorems · Theorem · general topology
Filter.disjoint_of_disjoint_of_mem
∀ {α : Type u} {f g : Filter α} {s t : Set α}, Disjoint s t → s ∈ f → t ∈ g → Disjoint f g- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 61 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
- Disjointstatement and proof · cited by 2,201
- Filter.disjoint_iffproof · cited by 5
Cited by15
Results whose statement or proof uses this declaration.
- Metric.disjoint_nhds_coboundedproof · cited by 7
- regularSpace_TFAEproof · cited by 6
- Filter.nonneg_sub_iffproof · cited by 2
- Filter.disjoint_atBot_atTopproof · cited by 2
- Filter.disjoint_atBot_principal_Iciproof · cited by 2
- Filter.disjoint_atTop_atBotproof · cited by 2
- isOpen_setOfPred_disjoint_nhds_nhdsproof · cited by 1
- Filter.one_le_div_iffproof · cited by 1
- Filter.disjoint_atTop_principal_Iicproof · cited by 1
- disjoint_nhds_atTop_iffproof · cited by 1
- Filter.disjoint_atBot_principal_Ioiproof · cited by 0
- Filter.disjoint_atTop_principal_Iioproof · cited by 0